Algebra Beispiele

$1 + \cos (18 x)$

Schritt 1

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.1

Faktorisiere $2$ aus $18 x$ heraus.

$1 + \cos (2 (9 x))$

Schritt 1.2

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.1

Faktorisiere $3$ aus $9 x$ heraus.

$1 + 2 \cos^{2} (3 (3 x)) - 1$

Schritt 1.2.2

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.1

Benutze die Dreifachwinkelfunktion, um $\cos (3 x)$ in $4 \cos^{3} (x) - 3 \cos (x)$ umzuformen.

$1 + 2 {(4 {(4 \cos^{3} (x) - 3 \cos (x))}^{3} - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.2

Wende den binomischen Lehrsatz an.

$1 + 2 {(4 ({(4 \cos^{3} (x))}^{3} + 3 {(4 \cos^{3} (x))}^{2} (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.3.1

Wende die Produktregel auf $4 \cos^{3} (x)$ an.

$1 + 2 {(4 (4^{3} {(\cos^{3} (x))}^{3} + 3 {(4 \cos^{3} (x))}^{2} (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.2

Potenziere $4$ mit $3$ .

$1 + 2 {(4 (64 {(\cos^{3} (x))}^{3} + 3 {(4 \cos^{3} (x))}^{2} (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.3

Multipliziere die Exponenten in ${(\cos^{3} (x))}^{3}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.3.3.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

$1 + 2 {(4 (64 {\cos (x)}^{3 \cdot 3} + 3 {(4 \cos^{3} (x))}^{2} (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.3.2

Mutltipliziere $3$ mit $3$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 {(4 \cos^{3} (x))}^{2} (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.4

Wende die Produktregel auf $4 \cos^{3} (x)$ an.

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (4^{2} {(\cos^{3} (x))}^{2}) (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.5

Potenziere $4$ mit $2$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 {(\cos^{3} (x))}^{2}) (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.6

Multipliziere die Exponenten in ${(\cos^{3} (x))}^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.3.6.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 {\cos (x)}^{3 \cdot 2}) (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.6.2

Mutltipliziere $3$ mit $2$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 \cos^{6} (x)) (- 3 \cos (x)) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.7

Multipliziere $\cos^{6} (x)$ mit $\cos (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.3.7.1

Bewege $\cos (x)$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 (\cos (x) \cos^{6} (x))) \cdot - 3 + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.7.2

Mutltipliziere $\cos (x)$ mit $\cos^{6} (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.3.7.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 (\cos^{1} (x) \cos^{6} (x))) \cdot - 3 + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.7.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 {\cos (x)}^{1 + 6}) \cdot - 3 + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.7.3

Addiere $1$ und $6$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 3 (16 \cos^{7} (x)) \cdot - 3 + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.8

Mutltipliziere $16$ mit $3$ .

$1 + 2 {(4 (64 \cos^{9} (x) + 48 \cos^{7} (x) \cdot - 3 + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.9

Mutltipliziere $- 3$ mit $48$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 3 (4 \cos^{3} (x)) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.10

Mutltipliziere $4$ mit $3$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cos^{3} (x) {(- 3 \cos (x))}^{2} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.11

Wende die Produktregel auf $- 3 \cos (x)$ an.

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cos^{3} (x) ({(- 3)}^{2} \cos^{2} (x)) + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.12

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cdot {(- 3)}^{2} \cos^{3} (x) \cos^{2} (x) + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.13

Multipliziere $\cos^{3} (x)$ mit $\cos^{2} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.3.13.1

Bewege $\cos^{2} (x)$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cdot {(- 3)}^{2} (\cos^{2} (x) \cos^{3} (x)) + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.13.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cdot {(- 3)}^{2} {\cos (x)}^{2 + 3} + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.13.3

Addiere $2$ und $3$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cdot {(- 3)}^{2} \cos^{5} (x) + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.14

Potenziere $- 3$ mit $2$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 12 \cdot 9 \cos^{5} (x) + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.15

Mutltipliziere $12$ mit $9$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 108 \cos^{5} (x) + {(- 3 \cos (x))}^{3}) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.16

Wende die Produktregel auf $- 3 \cos (x)$ an.

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 108 \cos^{5} (x) + {(- 3)}^{3} \cos^{3} (x)) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.3.17

Potenziere $- 3$ mit $3$ .

$1 + 2 {(4 (64 \cos^{9} (x) - 144 \cos^{7} (x) + 108 \cos^{5} (x) - 27 \cos^{3} (x)) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.4

Wende das Distributivgesetz an.

$1 + 2 {(4 (64 \cos^{9} (x)) + 4 (- 144 \cos^{7} (x)) + 4 (108 \cos^{5} (x)) + 4 (- 27 \cos^{3} (x)) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.5

Vereinfache.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.2.5.1

Mutltipliziere $64$ mit $4$ .

$1 + 2 {(256 \cos^{9} (x) + 4 (- 144 \cos^{7} (x)) + 4 (108 \cos^{5} (x)) + 4 (- 27 \cos^{3} (x)) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.5.2

Mutltipliziere $- 144$ mit $4$ .

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 4 (108 \cos^{5} (x)) + 4 (- 27 \cos^{3} (x)) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.5.3

Mutltipliziere $108$ mit $4$ .

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) + 4 (- 27 \cos^{3} (x)) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.5.4

Mutltipliziere $- 27$ mit $4$ .

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 108 \cos^{3} (x) - 3 \cos (3 x))}^{2} - 1$

Schritt 1.2.2.6

Benutze die Dreifachwinkelfunktion, um $\cos (3 x)$ in $4 \cos^{3} (x) - 3 \cos (x)$ umzuformen.

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 108 \cos^{3} (x) - 3 (4 \cos^{3} (x) - 3 \cos (x)))}^{2} - 1$

Schritt 1.2.2.7

Wende das Distributivgesetz an.

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 108 \cos^{3} (x) - 3 (4 \cos^{3} (x)) - 3 (- 3 \cos (x)))}^{2} - 1$

Schritt 1.2.2.8

Mutltipliziere $4$ mit $- 3$ .

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 108 \cos^{3} (x) - 12 \cos^{3} (x) - 3 (- 3 \cos (x)))}^{2} - 1$

Schritt 1.2.2.9

Mutltipliziere $- 3$ mit $- 3$ .

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 108 \cos^{3} (x) - 12 \cos^{3} (x) + 9 \cos (x))}^{2} - 1$

Schritt 1.2.3

Subtrahiere $12 \cos^{3} (x)$ von $- 108 \cos^{3} (x)$ .

$1 + 2 {(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))}^{2} - 1$

Schritt 1.2.4

Schreibe ${(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))}^{2}$ als $(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x)) (256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))$ um.

$1 + 2 ((256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x)) (256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))) - 1$

Schritt 1.2.5

Multipliziere $(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x)) (256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))$ aus durch Multiplizieren jedes Terms des ersten Ausdrucks mit jedem Term des zweiten Ausdrucks.

$1 + 2 (256 \cos^{9} (x) (256 \cos^{9} (x)) + 256 \cos^{9} (x) (- 576 \cos^{7} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (256 \cdot 256 \cos^{9} (x) \cos^{9} (x) + 256 \cos^{9} (x) (- 576 \cos^{7} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.2

Multipliziere $\cos^{9} (x)$ mit $\cos^{9} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.2.1

Bewege $\cos^{9} (x)$ .

$1 + 2 (256 \cdot 256 (\cos^{9} (x) \cos^{9} (x)) + 256 \cos^{9} (x) (- 576 \cos^{7} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (256 \cdot 256 {\cos (x)}^{9 + 9} + 256 \cos^{9} (x) (- 576 \cos^{7} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.2.3

Addiere $9$ und $9$ .

$1 + 2 (256 \cdot 256 \cos^{18} (x) + 256 \cos^{9} (x) (- 576 \cos^{7} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.3

Mutltipliziere $256$ mit $256$ .

$1 + 2 (65536 \cos^{18} (x) + 256 \cos^{9} (x) (- 576 \cos^{7} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.4

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) + 256 \cdot - 576 \cos^{9} (x) \cos^{7} (x) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.5

Multipliziere $\cos^{9} (x)$ mit $\cos^{7} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.5.1

Bewege $\cos^{7} (x)$ .

$1 + 2 (65536 \cos^{18} (x) + 256 \cdot - 576 (\cos^{7} (x) \cos^{9} (x)) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.5.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) + 256 \cdot - 576 {\cos (x)}^{7 + 9} + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.5.3

Addiere $7$ und $9$ .

$1 + 2 (65536 \cos^{18} (x) + 256 \cdot - 576 \cos^{16} (x) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.6

Mutltipliziere $256$ mit $- 576$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 256 \cos^{9} (x) (432 \cos^{5} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.7

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 256 \cdot 432 \cos^{9} (x) \cos^{5} (x) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.8

Multipliziere $\cos^{9} (x)$ mit $\cos^{5} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.8.1

Bewege $\cos^{5} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 256 \cdot 432 (\cos^{5} (x) \cos^{9} (x)) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.8.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 256 \cdot 432 {\cos (x)}^{5 + 9} + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.8.3

Addiere $5$ und $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 256 \cdot 432 \cos^{14} (x) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.9

Mutltipliziere $256$ mit $432$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) + 256 \cos^{9} (x) (- 120 \cos^{3} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.10

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) + 256 \cdot - 120 \cos^{9} (x) \cos^{3} (x) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.11

Multipliziere $\cos^{9} (x)$ mit $\cos^{3} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.11.1

Bewege $\cos^{3} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) + 256 \cdot - 120 (\cos^{3} (x) \cos^{9} (x)) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.11.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) + 256 \cdot - 120 {\cos (x)}^{3 + 9} + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.11.3

Addiere $3$ und $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) + 256 \cdot - 120 \cos^{12} (x) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.12

Mutltipliziere $256$ mit $- 120$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 256 \cos^{9} (x) (9 \cos (x)) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.13

Multipliziere $\cos^{9} (x)$ mit $\cos (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.13.1

Bewege $\cos (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 256 (\cos (x) \cos^{9} (x)) \cdot 9 - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.13.2

Mutltipliziere $\cos (x)$ mit $\cos^{9} (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.13.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 256 (\cos^{1} (x) \cos^{9} (x)) \cdot 9 - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.13.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 256 {\cos (x)}^{1 + 9} \cdot 9 - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.13.3

Addiere $1$ und $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 256 \cos^{10} (x) \cdot 9 - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.14

Mutltipliziere $9$ mit $256$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 576 \cos^{7} (x) (256 \cos^{9} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.15

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 576 \cdot 256 \cos^{7} (x) \cos^{9} (x) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.16

Multipliziere $\cos^{7} (x)$ mit $\cos^{9} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.16.1

Bewege $\cos^{9} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 576 \cdot 256 (\cos^{9} (x) \cos^{7} (x)) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.16.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 576 \cdot 256 {\cos (x)}^{9 + 7} - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.16.3

Addiere $9$ und $7$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 576 \cdot 256 \cos^{16} (x) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.17

Mutltipliziere $- 576$ mit $256$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) - 576 \cos^{7} (x) (- 576 \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.18

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) - 576 \cdot - 576 \cos^{7} (x) \cos^{7} (x) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.19

Multipliziere $\cos^{7} (x)$ mit $\cos^{7} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.19.1

Bewege $\cos^{7} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) - 576 \cdot - 576 (\cos^{7} (x) \cos^{7} (x)) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.19.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) - 576 \cdot - 576 {\cos (x)}^{7 + 7} - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.19.3

Addiere $7$ und $7$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) - 576 \cdot - 576 \cos^{14} (x) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.20

Mutltipliziere $- 576$ mit $- 576$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 576 \cos^{7} (x) (432 \cos^{5} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.21

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 576 \cdot 432 \cos^{7} (x) \cos^{5} (x) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.22

Multipliziere $\cos^{7} (x)$ mit $\cos^{5} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.22.1

Bewege $\cos^{5} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 576 \cdot 432 (\cos^{5} (x) \cos^{7} (x)) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.22.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 576 \cdot 432 {\cos (x)}^{5 + 7} - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.22.3

Addiere $5$ und $7$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 576 \cdot 432 \cos^{12} (x) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.23

Mutltipliziere $- 576$ mit $432$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) - 576 \cos^{7} (x) (- 120 \cos^{3} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.24

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) - 576 \cdot - 120 \cos^{7} (x) \cos^{3} (x) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.25

Multipliziere $\cos^{7} (x)$ mit $\cos^{3} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.25.1

Bewege $\cos^{3} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) - 576 \cdot - 120 (\cos^{3} (x) \cos^{7} (x)) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.25.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) - 576 \cdot - 120 {\cos (x)}^{3 + 7} - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.25.3

Addiere $3$ und $7$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) - 576 \cdot - 120 \cos^{10} (x) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.26

Mutltipliziere $- 576$ mit $- 120$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 576 \cos^{7} (x) (9 \cos (x)) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.27

Multipliziere $\cos^{7} (x)$ mit $\cos (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.27.1

Bewege $\cos (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 576 (\cos (x) \cos^{7} (x)) \cdot 9 + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.27.2

Mutltipliziere $\cos (x)$ mit $\cos^{7} (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.27.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 576 (\cos^{1} (x) \cos^{7} (x)) \cdot 9 + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.27.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 576 {\cos (x)}^{1 + 7} \cdot 9 + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.27.3

Addiere $1$ und $7$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 576 \cos^{8} (x) \cdot 9 + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.28

Mutltipliziere $9$ mit $- 576$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 432 \cos^{5} (x) (256 \cos^{9} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.29

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 432 \cdot 256 \cos^{5} (x) \cos^{9} (x) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.30

Multipliziere $\cos^{5} (x)$ mit $\cos^{9} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.30.1

Bewege $\cos^{9} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 432 \cdot 256 (\cos^{9} (x) \cos^{5} (x)) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.30.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 432 \cdot 256 {\cos (x)}^{9 + 5} + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.30.3

Addiere $9$ und $5$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 432 \cdot 256 \cos^{14} (x) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.31

Mutltipliziere $432$ mit $256$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) + 432 \cos^{5} (x) (- 576 \cos^{7} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.32

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) + 432 \cdot - 576 \cos^{5} (x) \cos^{7} (x) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.33

Multipliziere $\cos^{5} (x)$ mit $\cos^{7} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.33.1

Bewege $\cos^{7} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) + 432 \cdot - 576 (\cos^{7} (x) \cos^{5} (x)) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.33.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) + 432 \cdot - 576 {\cos (x)}^{7 + 5} + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.33.3

Addiere $7$ und $5$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) + 432 \cdot - 576 \cos^{12} (x) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.34

Mutltipliziere $432$ mit $- 576$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 432 \cos^{5} (x) (432 \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.35

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 432 \cdot 432 \cos^{5} (x) \cos^{5} (x) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.36

Multipliziere $\cos^{5} (x)$ mit $\cos^{5} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.36.1

Bewege $\cos^{5} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 432 \cdot 432 (\cos^{5} (x) \cos^{5} (x)) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.36.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 432 \cdot 432 {\cos (x)}^{5 + 5} + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.36.3

Addiere $5$ und $5$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 432 \cdot 432 \cos^{10} (x) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.37

Mutltipliziere $432$ mit $432$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) + 432 \cos^{5} (x) (- 120 \cos^{3} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.38

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) + 432 \cdot - 120 \cos^{5} (x) \cos^{3} (x) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.39

Multipliziere $\cos^{5} (x)$ mit $\cos^{3} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.39.1

Bewege $\cos^{3} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) + 432 \cdot - 120 (\cos^{3} (x) \cos^{5} (x)) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.39.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) + 432 \cdot - 120 {\cos (x)}^{3 + 5} + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.39.3

Addiere $3$ und $5$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) + 432 \cdot - 120 \cos^{8} (x) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.40

Mutltipliziere $432$ mit $- 120$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 432 \cos^{5} (x) (9 \cos (x)) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.41

Multipliziere $\cos^{5} (x)$ mit $\cos (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.41.1

Bewege $\cos (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 432 (\cos (x) \cos^{5} (x)) \cdot 9 - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.41.2

Mutltipliziere $\cos (x)$ mit $\cos^{5} (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.41.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 432 (\cos^{1} (x) \cos^{5} (x)) \cdot 9 - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.41.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 432 {\cos (x)}^{1 + 5} \cdot 9 - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.41.3

Addiere $1$ und $5$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 432 \cos^{6} (x) \cdot 9 - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.42

Mutltipliziere $9$ mit $432$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 120 \cos^{3} (x) (256 \cos^{9} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.43

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 120 \cdot 256 \cos^{3} (x) \cos^{9} (x) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.44

Multipliziere $\cos^{3} (x)$ mit $\cos^{9} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.44.1

Bewege $\cos^{9} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 120 \cdot 256 (\cos^{9} (x) \cos^{3} (x)) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.44.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 120 \cdot 256 {\cos (x)}^{9 + 3} - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.44.3

Addiere $9$ und $3$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 120 \cdot 256 \cos^{12} (x) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.45

Mutltipliziere $- 120$ mit $256$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) - 120 \cos^{3} (x) (- 576 \cos^{7} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.46

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) - 120 \cdot - 576 \cos^{3} (x) \cos^{7} (x) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.47

Multipliziere $\cos^{3} (x)$ mit $\cos^{7} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.47.1

Bewege $\cos^{7} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) - 120 \cdot - 576 (\cos^{7} (x) \cos^{3} (x)) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.47.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) - 120 \cdot - 576 {\cos (x)}^{7 + 3} - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.47.3

Addiere $7$ und $3$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) - 120 \cdot - 576 \cos^{10} (x) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.48

Mutltipliziere $- 120$ mit $- 576$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 120 \cos^{3} (x) (432 \cos^{5} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.49

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 120 \cdot 432 \cos^{3} (x) \cos^{5} (x) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.50

Multipliziere $\cos^{3} (x)$ mit $\cos^{5} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.50.1

Bewege $\cos^{5} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 120 \cdot 432 (\cos^{5} (x) \cos^{3} (x)) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.50.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 120 \cdot 432 {\cos (x)}^{5 + 3} - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.50.3

Addiere $5$ und $3$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 120 \cdot 432 \cos^{8} (x) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.51

Mutltipliziere $- 120$ mit $432$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) - 120 \cos^{3} (x) (- 120 \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.52

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) - 120 \cdot - 120 \cos^{3} (x) \cos^{3} (x) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.53

Multipliziere $\cos^{3} (x)$ mit $\cos^{3} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.53.1

Bewege $\cos^{3} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) - 120 \cdot - 120 (\cos^{3} (x) \cos^{3} (x)) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.53.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) - 120 \cdot - 120 {\cos (x)}^{3 + 3} - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.53.3

Addiere $3$ und $3$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) - 120 \cdot - 120 \cos^{6} (x) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.54

Mutltipliziere $- 120$ mit $- 120$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 120 \cos^{3} (x) (9 \cos (x)) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.55

Multipliziere $\cos^{3} (x)$ mit $\cos (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.55.1

Bewege $\cos (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 120 (\cos (x) \cos^{3} (x)) \cdot 9 + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.55.2

Mutltipliziere $\cos (x)$ mit $\cos^{3} (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.55.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 120 (\cos^{1} (x) \cos^{3} (x)) \cdot 9 + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.55.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 120 {\cos (x)}^{1 + 3} \cdot 9 + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.55.3

Addiere $1$ und $3$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 120 \cos^{4} (x) \cdot 9 + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.56

Mutltipliziere $9$ mit $- 120$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 9 \cos (x) (256 \cos^{9} (x)) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.57

Multipliziere $\cos (x)$ mit $\cos^{9} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.57.1

Bewege $\cos^{9} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 9 (\cos^{9} (x) \cos (x)) \cdot 256 + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.57.2

Mutltipliziere $\cos^{9} (x)$ mit $\cos (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.57.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 9 (\cos^{9} (x) \cos^{1} (x)) \cdot 256 + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.57.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 9 {\cos (x)}^{9 + 1} \cdot 256 + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.57.3

Addiere $9$ und $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 9 \cos^{10} (x) \cdot 256 + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.58

Mutltipliziere $256$ mit $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) + 9 \cos (x) (- 576 \cos^{7} (x)) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.59

Multipliziere $\cos (x)$ mit $\cos^{7} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.59.1

Bewege $\cos^{7} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) + 9 (\cos^{7} (x) \cos (x)) \cdot - 576 + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.59.2

Mutltipliziere $\cos^{7} (x)$ mit $\cos (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.59.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) + 9 (\cos^{7} (x) \cos^{1} (x)) \cdot - 576 + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.59.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) + 9 {\cos (x)}^{7 + 1} \cdot - 576 + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.59.3

Addiere $7$ und $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) + 9 \cos^{8} (x) \cdot - 576 + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.60

Mutltipliziere $- 576$ mit $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 9 \cos (x) (432 \cos^{5} (x)) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.61

Multipliziere $\cos (x)$ mit $\cos^{5} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.61.1

Bewege $\cos^{5} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 9 (\cos^{5} (x) \cos (x)) \cdot 432 + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.61.2

Mutltipliziere $\cos^{5} (x)$ mit $\cos (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.61.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 9 (\cos^{5} (x) \cos^{1} (x)) \cdot 432 + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.61.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 9 {\cos (x)}^{5 + 1} \cdot 432 + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.61.3

Addiere $5$ und $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 9 \cos^{6} (x) \cdot 432 + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.62

Mutltipliziere $432$ mit $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) + 9 \cos (x) (- 120 \cos^{3} (x)) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.63

Multipliziere $\cos (x)$ mit $\cos^{3} (x)$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.63.1

Bewege $\cos^{3} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) + 9 (\cos^{3} (x) \cos (x)) \cdot - 120 + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.63.2

Mutltipliziere $\cos^{3} (x)$ mit $\cos (x)$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.63.2.1

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) + 9 (\cos^{3} (x) \cos^{1} (x)) \cdot - 120 + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.63.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) + 9 {\cos (x)}^{3 + 1} \cdot - 120 + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.63.3

Addiere $3$ und $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) + 9 \cos^{4} (x) \cdot - 120 + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.64

Mutltipliziere $- 120$ mit $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 9 \cos (x) (9 \cos (x))) - 1$

Schritt 1.2.6.65

Multipliziere $9 \cos (x) (9 \cos (x))$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.6.65.1

Mutltipliziere $9$ mit $9$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos (x) \cos (x)) - 1$

Schritt 1.2.6.65.2

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 (\cos^{1} (x) \cos (x))) - 1$

Schritt 1.2.6.65.3

Potenziere $\cos (x)$ mit $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 (\cos^{1} (x) \cos^{1} (x))) - 1$

Schritt 1.2.6.65.4

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 {\cos (x)}^{1 + 1}) - 1$

Schritt 1.2.6.65.5

Addiere $1$ und $1$ .

$1 + 2 (65536 \cos^{18} (x) - 147456 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 147456 \cos^{16} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.7

Subtrahiere $147456 \cos^{16} (x)$ von $- 147456 \cos^{16} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 110592 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) + 331776 \cos^{14} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.8

Addiere $110592 \cos^{14} (x)$ und $331776 \cos^{14} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 442368 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 110592 \cos^{14} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.9

Addiere $442368 \cos^{14} (x)$ und $110592 \cos^{14} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 30720 \cos^{12} (x) + 2304 \cos^{10} (x) - 248832 \cos^{12} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.10

Subtrahiere $248832 \cos^{12} (x)$ von $- 30720 \cos^{12} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 279552 \cos^{12} (x) + 2304 \cos^{10} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) - 248832 \cos^{12} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.11

Subtrahiere $248832 \cos^{12} (x)$ von $- 279552 \cos^{12} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 528384 \cos^{12} (x) + 2304 \cos^{10} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 30720 \cos^{12} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.12

Subtrahiere $30720 \cos^{12} (x)$ von $- 528384 \cos^{12} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 2304 \cos^{10} (x) + 69120 \cos^{10} (x) - 5184 \cos^{8} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.13

Addiere $2304 \cos^{10} (x)$ und $69120 \cos^{10} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 71424 \cos^{10} (x) - 5184 \cos^{8} (x) + 186624 \cos^{10} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.14

Addiere $71424 \cos^{10} (x)$ und $186624 \cos^{10} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 258048 \cos^{10} (x) - 5184 \cos^{8} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) + 69120 \cos^{10} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.15

Addiere $258048 \cos^{10} (x)$ und $69120 \cos^{10} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 327168 \cos^{10} (x) - 5184 \cos^{8} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 2304 \cos^{10} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.16

Addiere $327168 \cos^{10} (x)$ und $2304 \cos^{10} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 5184 \cos^{8} (x) - 51840 \cos^{8} (x) + 3888 \cos^{6} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.17

Subtrahiere $51840 \cos^{8} (x)$ von $- 5184 \cos^{8} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 57024 \cos^{8} (x) + 3888 \cos^{6} (x) - 51840 \cos^{8} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.18

Subtrahiere $51840 \cos^{8} (x)$ von $- 57024 \cos^{8} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 108864 \cos^{8} (x) + 3888 \cos^{6} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) - 5184 \cos^{8} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.19

Subtrahiere $5184 \cos^{8} (x)$ von $- 108864 \cos^{8} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 114048 \cos^{8} (x) + 3888 \cos^{6} (x) + 14400 \cos^{6} (x) - 1080 \cos^{4} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.20

Addiere $3888 \cos^{6} (x)$ und $14400 \cos^{6} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 114048 \cos^{8} (x) + 18288 \cos^{6} (x) - 1080 \cos^{4} (x) + 3888 \cos^{6} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.21

Addiere $18288 \cos^{6} (x)$ und $3888 \cos^{6} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 114048 \cos^{8} (x) + 22176 \cos^{6} (x) - 1080 \cos^{4} (x) - 1080 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.22

Subtrahiere $1080 \cos^{4} (x)$ von $- 1080 \cos^{4} (x)$ .

$1 + 2 (65536 \cos^{18} (x) - 294912 \cos^{16} (x) + 552960 \cos^{14} (x) - 559104 \cos^{12} (x) + 329472 \cos^{10} (x) - 114048 \cos^{8} (x) + 22176 \cos^{6} (x) - 2160 \cos^{4} (x) + 81 \cos^{2} (x)) - 1$

Schritt 1.2.23

Wende das Distributivgesetz an.

$1 + 2 (65536 \cos^{18} (x)) + 2 (- 294912 \cos^{16} (x)) + 2 (552960 \cos^{14} (x)) + 2 (- 559104 \cos^{12} (x)) + 2 (329472 \cos^{10} (x)) + 2 (- 114048 \cos^{8} (x)) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24

Vereinfache.

Tippen, um mehr Schritte zu sehen ...

Schritt 1.2.24.1

Mutltipliziere $65536$ mit $2$ .

$1 + 131072 \cos^{18} (x) + 2 (- 294912 \cos^{16} (x)) + 2 (552960 \cos^{14} (x)) + 2 (- 559104 \cos^{12} (x)) + 2 (329472 \cos^{10} (x)) + 2 (- 114048 \cos^{8} (x)) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.2

Mutltipliziere $- 294912$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 2 (552960 \cos^{14} (x)) + 2 (- 559104 \cos^{12} (x)) + 2 (329472 \cos^{10} (x)) + 2 (- 114048 \cos^{8} (x)) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.3

Mutltipliziere $552960$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) + 2 (- 559104 \cos^{12} (x)) + 2 (329472 \cos^{10} (x)) + 2 (- 114048 \cos^{8} (x)) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.4

Mutltipliziere $- 559104$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 2 (329472 \cos^{10} (x)) + 2 (- 114048 \cos^{8} (x)) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.5

Mutltipliziere $329472$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) + 2 (- 114048 \cos^{8} (x)) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.6

Mutltipliziere $- 114048$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 2 (22176 \cos^{6} (x)) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.7

Mutltipliziere $22176$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) + 2 (- 2160 \cos^{4} (x)) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.8

Mutltipliziere $- 2160$ mit $2$ .

$1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) - 4320 \cos^{4} (x) + 2 (81 \cos^{2} (x)) - 1$

Schritt 1.2.24.9

Mutltipliziere $81$ mit $2$ .

Schritt 2

Vereine die Terme mit entgegengesetztem Vorzeichen in $1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) - 4320 \cos^{4} (x) + 162 \cos^{2} (x) - 1$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 2.1

Subtrahiere $1$ von $1$ .

$0 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) - 4320 \cos^{4} (x) + 162 \cos^{2} (x)$

Schritt 2.2

Addiere $0$ und $131072 \cos^{18} (x)$ .

$131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) - 4320 \cos^{4} (x) + 162 \cos^{2} (x)$