Algèbre Exemples

$1 + \cos (18 x)$

Étape 1

Simplifiez chaque terme.

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Étape 1.1

Factorisez $2$ à partir de $18 x$ .

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

Étape 1.2

Simplifiez chaque terme.

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Étape 1.2.1

Factorisez $3$ à partir de $9 x$ .

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

Étape 1.2.2

Simplifiez chaque terme.

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Étape 1.2.2.1

Utilisez l’identité d’angle triple pour transformer $\cos (3 x)$ en $4 \cos^{3} (x) - 3 \cos (x)$ .

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

Étape 1.2.2.2

Utilisez le théorème du binôme.

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

Étape 1.2.2.3

Simplifiez chaque terme.

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Étape 1.2.2.3.1

Appliquez la règle de produit à $4 \cos^{3} (x)$ .

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

Étape 1.2.2.3.2

Élevez $4$ à la puissance $3$ .

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

Étape 1.2.2.3.3

Multipliez les exposants dans ${(\cos^{3} (x))}^{3}$ .

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Étape 1.2.2.3.3.1

Appliquez la règle de puissance et multipliez les exposants, ${(a^{m})}^{n} = a^{m n}$ .

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

Étape 1.2.2.3.3.2

Multipliez $3$ par $3$ .

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

Étape 1.2.2.3.4

Appliquez la règle de produit à $4 \cos^{3} (x)$ .

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

Étape 1.2.2.3.5

Élevez $4$ à la puissance $2$ .

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

Étape 1.2.2.3.6

Multipliez les exposants dans ${(\cos^{3} (x))}^{2}$ .

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Étape 1.2.2.3.6.1

Appliquez la règle de puissance et multipliez les exposants, ${(a^{m})}^{n} = a^{m n}$ .

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

Étape 1.2.2.3.6.2

Multipliez $3$ par $2$ .

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

Étape 1.2.2.3.7

Multipliez $\cos^{6} (x)$ par $\cos (x)$ en additionnant les exposants.

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Étape 1.2.2.3.7.1

Déplacez $\cos (x)$ .

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

Étape 1.2.2.3.7.2

Multipliez $\cos (x)$ par $\cos^{6} (x)$ .

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Étape 1.2.2.3.7.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.2.3.7.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.2.3.7.3

Additionnez $1$ et $6$ .

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

Étape 1.2.2.3.8

Multipliez $16$ par $3$ .

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

Étape 1.2.2.3.9

Multipliez $- 3$ par $48$ .

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

Étape 1.2.2.3.10

Multipliez $4$ par $3$ .

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

Étape 1.2.2.3.11

Appliquez la règle de produit à $- 3 \cos (x)$ .

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

Étape 1.2.2.3.12

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.2.3.13

Multipliez $\cos^{3} (x)$ par $\cos^{2} (x)$ en additionnant les exposants.

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Étape 1.2.2.3.13.1

Déplacez $\cos^{2} (x)$ .

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

Étape 1.2.2.3.13.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.2.3.13.3

Additionnez $2$ et $3$ .

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

Étape 1.2.2.3.14

Élevez $- 3$ à la puissance $2$ .

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

Étape 1.2.2.3.15

Multipliez $12$ par $9$ .

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

Étape 1.2.2.3.16

Appliquez la règle de produit à $- 3 \cos (x)$ .

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

Étape 1.2.2.3.17

Élevez $- 3$ à la puissance $3$ .

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

Étape 1.2.2.4

Appliquez la propriété distributive.

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

Étape 1.2.2.5

Simplifiez

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Étape 1.2.2.5.1

Multipliez $64$ par $4$ .

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

Étape 1.2.2.5.2

Multipliez $- 144$ par $4$ .

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

Étape 1.2.2.5.3

Multipliez $108$ par $4$ .

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

Étape 1.2.2.5.4

Multipliez $- 27$ par $4$ .

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

Étape 1.2.2.6

Utilisez l’identité d’angle triple pour transformer $\cos (3 x)$ en $4 \cos^{3} (x) - 3 \cos (x)$ .

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

Étape 1.2.2.7

Appliquez la propriété distributive.

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

Étape 1.2.2.8

Multipliez $4$ par $- 3$ .

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

Étape 1.2.2.9

Multipliez $- 3$ par $- 3$ .

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

Étape 1.2.3

Soustrayez $12 \cos^{3} (x)$ de $- 108 \cos^{3} (x)$ .

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

Étape 1.2.4

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

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

Étape 1.2.5

Développez $(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x)) (256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))$ en multipliant chaque terme dans la première expression par chaque terme dans la deuxième expression.

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

Étape 1.2.6

Simplifiez chaque terme.

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Étape 1.2.6.1

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.2

Multipliez $\cos^{9} (x)$ par $\cos^{9} (x)$ en additionnant les exposants.

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Étape 1.2.6.2.1

Déplacez $\cos^{9} (x)$ .

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

Étape 1.2.6.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.2.3

Additionnez $9$ et $9$ .

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

Étape 1.2.6.3

Multipliez $256$ par $256$ .

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

Étape 1.2.6.4

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.5

Multipliez $\cos^{9} (x)$ par $\cos^{7} (x)$ en additionnant les exposants.

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Étape 1.2.6.5.1

Déplacez $\cos^{7} (x)$ .

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

Étape 1.2.6.5.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.5.3

Additionnez $7$ et $9$ .

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

Étape 1.2.6.6

Multipliez $256$ par $- 576$ .

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

Étape 1.2.6.7

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.8

Multipliez $\cos^{9} (x)$ par $\cos^{5} (x)$ en additionnant les exposants.

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Étape 1.2.6.8.1

Déplacez $\cos^{5} (x)$ .

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

Étape 1.2.6.8.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.8.3

Additionnez $5$ et $9$ .

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

Étape 1.2.6.9

Multipliez $256$ par $432$ .

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

Étape 1.2.6.10

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.11

Multipliez $\cos^{9} (x)$ par $\cos^{3} (x)$ en additionnant les exposants.

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Étape 1.2.6.11.1

Déplacez $\cos^{3} (x)$ .

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

Étape 1.2.6.11.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.11.3

Additionnez $3$ et $9$ .

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

Étape 1.2.6.12

Multipliez $256$ par $- 120$ .

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

Étape 1.2.6.13

Multipliez $\cos^{9} (x)$ par $\cos (x)$ en additionnant les exposants.

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Étape 1.2.6.13.1

Déplacez $\cos (x)$ .

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

Étape 1.2.6.13.2

Multipliez $\cos (x)$ par $\cos^{9} (x)$ .

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Étape 1.2.6.13.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.13.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.13.3

Additionnez $1$ et $9$ .

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

Étape 1.2.6.14

Multipliez $9$ par $256$ .

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

Étape 1.2.6.15

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.16

Multipliez $\cos^{7} (x)$ par $\cos^{9} (x)$ en additionnant les exposants.

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Étape 1.2.6.16.1

Déplacez $\cos^{9} (x)$ .

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

Étape 1.2.6.16.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.16.3

Additionnez $9$ et $7$ .

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

Étape 1.2.6.17

Multipliez $- 576$ par $256$ .

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

Étape 1.2.6.18

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.19

Multipliez $\cos^{7} (x)$ par $\cos^{7} (x)$ en additionnant les exposants.

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Étape 1.2.6.19.1

Déplacez $\cos^{7} (x)$ .

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

Étape 1.2.6.19.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.19.3

Additionnez $7$ et $7$ .

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

Étape 1.2.6.20

Multipliez $- 576$ par $- 576$ .

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

Étape 1.2.6.21

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.22

Multipliez $\cos^{7} (x)$ par $\cos^{5} (x)$ en additionnant les exposants.

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Étape 1.2.6.22.1

Déplacez $\cos^{5} (x)$ .

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

Étape 1.2.6.22.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.22.3

Additionnez $5$ et $7$ .

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

Étape 1.2.6.23

Multipliez $- 576$ par $432$ .

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

Étape 1.2.6.24

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.25

Multipliez $\cos^{7} (x)$ par $\cos^{3} (x)$ en additionnant les exposants.

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Étape 1.2.6.25.1

Déplacez $\cos^{3} (x)$ .

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

Étape 1.2.6.25.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.25.3

Additionnez $3$ et $7$ .

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

Étape 1.2.6.26

Multipliez $- 576$ par $- 120$ .

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

Étape 1.2.6.27

Multipliez $\cos^{7} (x)$ par $\cos (x)$ en additionnant les exposants.

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Étape 1.2.6.27.1

Déplacez $\cos (x)$ .

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

Étape 1.2.6.27.2

Multipliez $\cos (x)$ par $\cos^{7} (x)$ .

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Étape 1.2.6.27.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.27.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.27.3

Additionnez $1$ et $7$ .

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

Étape 1.2.6.28

Multipliez $9$ par $- 576$ .

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

Étape 1.2.6.29

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.30

Multipliez $\cos^{5} (x)$ par $\cos^{9} (x)$ en additionnant les exposants.

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Étape 1.2.6.30.1

Déplacez $\cos^{9} (x)$ .

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

Étape 1.2.6.30.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.30.3

Additionnez $9$ et $5$ .

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

Étape 1.2.6.31

Multipliez $432$ par $256$ .

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

Étape 1.2.6.32

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.33

Multipliez $\cos^{5} (x)$ par $\cos^{7} (x)$ en additionnant les exposants.

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Étape 1.2.6.33.1

Déplacez $\cos^{7} (x)$ .

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

Étape 1.2.6.33.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.33.3

Additionnez $7$ et $5$ .

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

Étape 1.2.6.34

Multipliez $432$ par $- 576$ .

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

Étape 1.2.6.35

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.36

Multipliez $\cos^{5} (x)$ par $\cos^{5} (x)$ en additionnant les exposants.

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Étape 1.2.6.36.1

Déplacez $\cos^{5} (x)$ .

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

Étape 1.2.6.36.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.36.3

Additionnez $5$ et $5$ .

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

Étape 1.2.6.37

Multipliez $432$ par $432$ .

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

Étape 1.2.6.38

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.39

Multipliez $\cos^{5} (x)$ par $\cos^{3} (x)$ en additionnant les exposants.

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Étape 1.2.6.39.1

Déplacez $\cos^{3} (x)$ .

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

Étape 1.2.6.39.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.39.3

Additionnez $3$ et $5$ .

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

Étape 1.2.6.40

Multipliez $432$ par $- 120$ .

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

Étape 1.2.6.41

Multipliez $\cos^{5} (x)$ par $\cos (x)$ en additionnant les exposants.

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Étape 1.2.6.41.1

Déplacez $\cos (x)$ .

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

Étape 1.2.6.41.2

Multipliez $\cos (x)$ par $\cos^{5} (x)$ .

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Étape 1.2.6.41.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.41.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.41.3

Additionnez $1$ et $5$ .

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

Étape 1.2.6.42

Multipliez $9$ par $432$ .

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

Étape 1.2.6.43

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.44

Multipliez $\cos^{3} (x)$ par $\cos^{9} (x)$ en additionnant les exposants.

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Étape 1.2.6.44.1

Déplacez $\cos^{9} (x)$ .

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

Étape 1.2.6.44.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.44.3

Additionnez $9$ et $3$ .

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

Étape 1.2.6.45

Multipliez $- 120$ par $256$ .

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

Étape 1.2.6.46

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.47

Multipliez $\cos^{3} (x)$ par $\cos^{7} (x)$ en additionnant les exposants.

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Étape 1.2.6.47.1

Déplacez $\cos^{7} (x)$ .

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

Étape 1.2.6.47.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.47.3

Additionnez $7$ et $3$ .

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

Étape 1.2.6.48

Multipliez $- 120$ par $- 576$ .

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

Étape 1.2.6.49

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.50

Multipliez $\cos^{3} (x)$ par $\cos^{5} (x)$ en additionnant les exposants.

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Étape 1.2.6.50.1

Déplacez $\cos^{5} (x)$ .

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

Étape 1.2.6.50.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.50.3

Additionnez $5$ et $3$ .

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

Étape 1.2.6.51

Multipliez $- 120$ par $432$ .

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

Étape 1.2.6.52

Réécrivez en utilisant la commutativité de la multiplication.

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

Étape 1.2.6.53

Multipliez $\cos^{3} (x)$ par $\cos^{3} (x)$ en additionnant les exposants.

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Étape 1.2.6.53.1

Déplacez $\cos^{3} (x)$ .

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

Étape 1.2.6.53.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.53.3

Additionnez $3$ et $3$ .

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

Étape 1.2.6.54

Multipliez $- 120$ par $- 120$ .

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

Étape 1.2.6.55

Multipliez $\cos^{3} (x)$ par $\cos (x)$ en additionnant les exposants.

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Étape 1.2.6.55.1

Déplacez $\cos (x)$ .

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

Étape 1.2.6.55.2

Multipliez $\cos (x)$ par $\cos^{3} (x)$ .

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Étape 1.2.6.55.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.55.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.55.3

Additionnez $1$ et $3$ .

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

Étape 1.2.6.56

Multipliez $9$ par $- 120$ .

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

Étape 1.2.6.57

Multipliez $\cos (x)$ par $\cos^{9} (x)$ en additionnant les exposants.

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Étape 1.2.6.57.1

Déplacez $\cos^{9} (x)$ .

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

Étape 1.2.6.57.2

Multipliez $\cos^{9} (x)$ par $\cos (x)$ .

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Étape 1.2.6.57.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.57.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.57.3

Additionnez $9$ et $1$ .

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

Étape 1.2.6.58

Multipliez $256$ par $9$ .

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

Étape 1.2.6.59

Multipliez $\cos (x)$ par $\cos^{7} (x)$ en additionnant les exposants.

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Étape 1.2.6.59.1

Déplacez $\cos^{7} (x)$ .

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

Étape 1.2.6.59.2

Multipliez $\cos^{7} (x)$ par $\cos (x)$ .

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Étape 1.2.6.59.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.59.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.59.3

Additionnez $7$ et $1$ .

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

Étape 1.2.6.60

Multipliez $- 576$ par $9$ .

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

Étape 1.2.6.61

Multipliez $\cos (x)$ par $\cos^{5} (x)$ en additionnant les exposants.

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Étape 1.2.6.61.1

Déplacez $\cos^{5} (x)$ .

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

Étape 1.2.6.61.2

Multipliez $\cos^{5} (x)$ par $\cos (x)$ .

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Étape 1.2.6.61.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.61.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.61.3

Additionnez $5$ et $1$ .

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

Étape 1.2.6.62

Multipliez $432$ par $9$ .

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

Étape 1.2.6.63

Multipliez $\cos (x)$ par $\cos^{3} (x)$ en additionnant les exposants.

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Étape 1.2.6.63.1

Déplacez $\cos^{3} (x)$ .

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

Étape 1.2.6.63.2

Multipliez $\cos^{3} (x)$ par $\cos (x)$ .

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Étape 1.2.6.63.2.1

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.63.2.2

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.63.3

Additionnez $3$ et $1$ .

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

Étape 1.2.6.64

Multipliez $- 120$ par $9$ .

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

Étape 1.2.6.65

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

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Étape 1.2.6.65.1

Multipliez $9$ par $9$ .

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

Étape 1.2.6.65.2

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.65.3

Élevez $\cos (x)$ à la puissance $1$ .

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

Étape 1.2.6.65.4

Utilisez la règle de puissance $a^{m} a^{n} = a^{m + n}$ pour associer des exposants.

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

Étape 1.2.6.65.5

Additionnez $1$ et $1$ .

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

Étape 1.2.7

Soustrayez $147456 \cos^{16} (x)$ de $- 147456 \cos^{16} (x)$ .

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

Étape 1.2.8

Additionnez $110592 \cos^{14} (x)$ et $331776 \cos^{14} (x)$ .

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

Étape 1.2.9

Additionnez $442368 \cos^{14} (x)$ et $110592 \cos^{14} (x)$ .

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

Étape 1.2.10

Soustrayez $248832 \cos^{12} (x)$ de $- 30720 \cos^{12} (x)$ .

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

Étape 1.2.11

Soustrayez $248832 \cos^{12} (x)$ de $- 279552 \cos^{12} (x)$ .

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

Étape 1.2.12

Soustrayez $30720 \cos^{12} (x)$ de $- 528384 \cos^{12} (x)$ .

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

Étape 1.2.13

Additionnez $2304 \cos^{10} (x)$ et $69120 \cos^{10} (x)$ .

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

Étape 1.2.14

Additionnez $71424 \cos^{10} (x)$ et $186624 \cos^{10} (x)$ .

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

Étape 1.2.15

Additionnez $258048 \cos^{10} (x)$ et $69120 \cos^{10} (x)$ .

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

Étape 1.2.16

Additionnez $327168 \cos^{10} (x)$ et $2304 \cos^{10} (x)$ .

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

Étape 1.2.17

Soustrayez $51840 \cos^{8} (x)$ de $- 5184 \cos^{8} (x)$ .

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

Étape 1.2.18

Soustrayez $51840 \cos^{8} (x)$ de $- 57024 \cos^{8} (x)$ .

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

Étape 1.2.19

Soustrayez $5184 \cos^{8} (x)$ de $- 108864 \cos^{8} (x)$ .

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

Étape 1.2.20

Additionnez $3888 \cos^{6} (x)$ et $14400 \cos^{6} (x)$ .

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

Étape 1.2.21

Additionnez $18288 \cos^{6} (x)$ et $3888 \cos^{6} (x)$ .

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

Étape 1.2.22

Soustrayez $1080 \cos^{4} (x)$ de $- 1080 \cos^{4} (x)$ .

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

Étape 1.2.23

Appliquez la propriété distributive.

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

Étape 1.2.24

Simplifiez

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Étape 1.2.24.1

Multipliez $65536$ par $2$ .

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

Étape 1.2.24.2

Multipliez $- 294912$ par $2$ .

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

Étape 1.2.24.3

Multipliez $552960$ par $2$ .

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

Étape 1.2.24.4

Multipliez $- 559104$ par $2$ .

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

Étape 1.2.24.5

Multipliez $329472$ par $2$ .

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

Étape 1.2.24.6

Multipliez $- 114048$ par $2$ .

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

Étape 1.2.24.7

Multipliez $22176$ par $2$ .

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

Étape 1.2.24.8

Multipliez $- 2160$ par $2$ .

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

Étape 1.2.24.9

Multipliez $81$ par $2$ .

Étape 2

Associez les termes opposés dans $1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) - 4320 \cos^{4} (x) + 162 \cos^{2} (x) - 1$ .

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Étape 2.1

Soustrayez $1$ de $1$ .

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

Étape 2.2

Additionnez $0$ et $131072 \cos^{18} (x)$ .

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