الجبر الأمثلة

$1 + \cos (18 x)$

خطوة 1

بسّط كل حد.

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خطوة 1.1

أخرِج العامل $2$ من $18 x$ .

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

خطوة 1.2

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خطوة 1.2.1

أخرِج العامل $3$ من $9 x$ .

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

خطوة 1.2.2

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خطوة 1.2.2.1

استخدِم المتطابقة ثلاثية الزوايا لتحويل $\cos (3 x)$ إلى $4 \cos^{3} (x) - 3 \cos (x)$ .

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

خطوة 1.2.2.2

استخدِم مبرهنة ذات الحدين.

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

خطوة 1.2.2.3

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خطوة 1.2.2.3.1

طبّق قاعدة الضرب على $4 \cos^{3} (x)$ .

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

خطوة 1.2.2.3.2

ارفع $4$ إلى القوة $3$ .

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

خطوة 1.2.2.3.3

اضرب الأُسس في ${(\cos^{3} (x))}^{3}$ .

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خطوة 1.2.2.3.3.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 1.2.2.3.3.2

اضرب $3$ في $3$ .

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

خطوة 1.2.2.3.4

طبّق قاعدة الضرب على $4 \cos^{3} (x)$ .

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

خطوة 1.2.2.3.5

ارفع $4$ إلى القوة $2$ .

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

خطوة 1.2.2.3.6

اضرب الأُسس في ${(\cos^{3} (x))}^{2}$ .

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خطوة 1.2.2.3.6.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 1.2.2.3.6.2

اضرب $3$ في $2$ .

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

خطوة 1.2.2.3.7

اضرب $\cos^{6} (x)$ في $\cos (x)$ بجمع الأُسس.

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خطوة 1.2.2.3.7.1

انقُل $\cos (x)$ .

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

خطوة 1.2.2.3.7.2

اضرب $\cos (x)$ في $\cos^{6} (x)$ .

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خطوة 1.2.2.3.7.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.2.3.7.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.2.3.7.3

أضف $1$ و $6$ .

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

خطوة 1.2.2.3.8

اضرب $16$ في $3$ .

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

خطوة 1.2.2.3.9

اضرب $- 3$ في $48$ .

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

خطوة 1.2.2.3.10

اضرب $4$ في $3$ .

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

خطوة 1.2.2.3.11

طبّق قاعدة الضرب على $- 3 \cos (x)$ .

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

خطوة 1.2.2.3.12

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.2.3.13

اضرب $\cos^{3} (x)$ في $\cos^{2} (x)$ بجمع الأُسس.

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خطوة 1.2.2.3.13.1

انقُل $\cos^{2} (x)$ .

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

خطوة 1.2.2.3.13.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.2.3.13.3

أضف $2$ و $3$ .

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

خطوة 1.2.2.3.14

ارفع $- 3$ إلى القوة $2$ .

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

خطوة 1.2.2.3.15

اضرب $12$ في $9$ .

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

خطوة 1.2.2.3.16

طبّق قاعدة الضرب على $- 3 \cos (x)$ .

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

خطوة 1.2.2.3.17

ارفع $- 3$ إلى القوة $3$ .

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

خطوة 1.2.2.4

طبّق خاصية التوزيع.

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

خطوة 1.2.2.5

بسّط.

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خطوة 1.2.2.5.1

اضرب $64$ في $4$ .

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

خطوة 1.2.2.5.2

اضرب $- 144$ في $4$ .

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

خطوة 1.2.2.5.3

اضرب $108$ في $4$ .

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

خطوة 1.2.2.5.4

اضرب $- 27$ في $4$ .

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

خطوة 1.2.2.6

استخدِم المتطابقة ثلاثية الزوايا لتحويل $\cos (3 x)$ إلى $4 \cos^{3} (x) - 3 \cos (x)$ .

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

خطوة 1.2.2.7

طبّق خاصية التوزيع.

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

خطوة 1.2.2.8

اضرب $4$ في $- 3$ .

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

خطوة 1.2.2.9

اضرب $- 3$ في $- 3$ .

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

خطوة 1.2.3

اطرح $12 \cos^{3} (x)$ من $- 108 \cos^{3} (x)$ .

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

خطوة 1.2.4

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

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

خطوة 1.2.5

وسّع $(256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x)) (256 \cos^{9} (x) - 576 \cos^{7} (x) + 432 \cos^{5} (x) - 120 \cos^{3} (x) + 9 \cos (x))$ بضرب كل حد في العبارة الأولى في كل حد في العبارة الثانية.

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

خطوة 1.2.6

بسّط كل حد.

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خطوة 1.2.6.1

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.2

اضرب $\cos^{9} (x)$ في $\cos^{9} (x)$ بجمع الأُسس.

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خطوة 1.2.6.2.1

انقُل $\cos^{9} (x)$ .

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

خطوة 1.2.6.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.2.3

أضف $9$ و $9$ .

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

خطوة 1.2.6.3

اضرب $256$ في $256$ .

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

خطوة 1.2.6.4

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.5

اضرب $\cos^{9} (x)$ في $\cos^{7} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.5.1

انقُل $\cos^{7} (x)$ .

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

خطوة 1.2.6.5.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.5.3

أضف $7$ و $9$ .

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

خطوة 1.2.6.6

اضرب $256$ في $- 576$ .

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

خطوة 1.2.6.7

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.8

اضرب $\cos^{9} (x)$ في $\cos^{5} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.8.1

انقُل $\cos^{5} (x)$ .

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

خطوة 1.2.6.8.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.8.3

أضف $5$ و $9$ .

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

خطوة 1.2.6.9

اضرب $256$ في $432$ .

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

خطوة 1.2.6.10

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.11

اضرب $\cos^{9} (x)$ في $\cos^{3} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.11.1

انقُل $\cos^{3} (x)$ .

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

خطوة 1.2.6.11.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.11.3

أضف $3$ و $9$ .

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

خطوة 1.2.6.12

اضرب $256$ في $- 120$ .

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

خطوة 1.2.6.13

اضرب $\cos^{9} (x)$ في $\cos (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.13.1

انقُل $\cos (x)$ .

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

خطوة 1.2.6.13.2

اضرب $\cos (x)$ في $\cos^{9} (x)$ .

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.13.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.13.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.13.3

أضف $1$ و $9$ .

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

خطوة 1.2.6.14

اضرب $9$ في $256$ .

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

خطوة 1.2.6.15

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.16

اضرب $\cos^{7} (x)$ في $\cos^{9} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.16.1

انقُل $\cos^{9} (x)$ .

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

خطوة 1.2.6.16.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.16.3

أضف $9$ و $7$ .

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

خطوة 1.2.6.17

اضرب $- 576$ في $256$ .

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

خطوة 1.2.6.18

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.19

اضرب $\cos^{7} (x)$ في $\cos^{7} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.19.1

انقُل $\cos^{7} (x)$ .

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

خطوة 1.2.6.19.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.19.3

أضف $7$ و $7$ .

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

خطوة 1.2.6.20

اضرب $- 576$ في $- 576$ .

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

خطوة 1.2.6.21

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.22

اضرب $\cos^{7} (x)$ في $\cos^{5} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.22.1

انقُل $\cos^{5} (x)$ .

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

خطوة 1.2.6.22.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.22.3

أضف $5$ و $7$ .

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

خطوة 1.2.6.23

اضرب $- 576$ في $432$ .

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

خطوة 1.2.6.24

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.25

اضرب $\cos^{7} (x)$ في $\cos^{3} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.25.1

انقُل $\cos^{3} (x)$ .

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

خطوة 1.2.6.25.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.25.3

أضف $3$ و $7$ .

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

خطوة 1.2.6.26

اضرب $- 576$ في $- 120$ .

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

خطوة 1.2.6.27

اضرب $\cos^{7} (x)$ في $\cos (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.27.1

انقُل $\cos (x)$ .

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

خطوة 1.2.6.27.2

اضرب $\cos (x)$ في $\cos^{7} (x)$ .

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.27.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.27.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.27.3

أضف $1$ و $7$ .

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

خطوة 1.2.6.28

اضرب $9$ في $- 576$ .

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

خطوة 1.2.6.29

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.30

اضرب $\cos^{5} (x)$ في $\cos^{9} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.30.1

انقُل $\cos^{9} (x)$ .

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

خطوة 1.2.6.30.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.30.3

أضف $9$ و $5$ .

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

خطوة 1.2.6.31

اضرب $432$ في $256$ .

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

خطوة 1.2.6.32

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.33

اضرب $\cos^{5} (x)$ في $\cos^{7} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.33.1

انقُل $\cos^{7} (x)$ .

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

خطوة 1.2.6.33.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.33.3

أضف $7$ و $5$ .

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

خطوة 1.2.6.34

اضرب $432$ في $- 576$ .

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

خطوة 1.2.6.35

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.36

اضرب $\cos^{5} (x)$ في $\cos^{5} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.36.1

انقُل $\cos^{5} (x)$ .

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

خطوة 1.2.6.36.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.36.3

أضف $5$ و $5$ .

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

خطوة 1.2.6.37

اضرب $432$ في $432$ .

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

خطوة 1.2.6.38

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.39

اضرب $\cos^{5} (x)$ في $\cos^{3} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.39.1

انقُل $\cos^{3} (x)$ .

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

خطوة 1.2.6.39.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.39.3

أضف $3$ و $5$ .

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

خطوة 1.2.6.40

اضرب $432$ في $- 120$ .

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

خطوة 1.2.6.41

اضرب $\cos^{5} (x)$ في $\cos (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.41.1

انقُل $\cos (x)$ .

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

خطوة 1.2.6.41.2

اضرب $\cos (x)$ في $\cos^{5} (x)$ .

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.41.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.41.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.41.3

أضف $1$ و $5$ .

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

خطوة 1.2.6.42

اضرب $9$ في $432$ .

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

خطوة 1.2.6.43

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.44

اضرب $\cos^{3} (x)$ في $\cos^{9} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.44.1

انقُل $\cos^{9} (x)$ .

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

خطوة 1.2.6.44.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.44.3

أضف $9$ و $3$ .

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

خطوة 1.2.6.45

اضرب $- 120$ في $256$ .

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

خطوة 1.2.6.46

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.47

اضرب $\cos^{3} (x)$ في $\cos^{7} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.47.1

انقُل $\cos^{7} (x)$ .

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

خطوة 1.2.6.47.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.47.3

أضف $7$ و $3$ .

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

خطوة 1.2.6.48

اضرب $- 120$ في $- 576$ .

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

خطوة 1.2.6.49

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.50

اضرب $\cos^{3} (x)$ في $\cos^{5} (x)$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

خطوة 1.2.6.50.1

انقُل $\cos^{5} (x)$ .

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

خطوة 1.2.6.50.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.50.3

أضف $5$ و $3$ .

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

خطوة 1.2.6.51

اضرب $- 120$ في $432$ .

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

خطوة 1.2.6.52

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

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

خطوة 1.2.6.53

اضرب $\cos^{3} (x)$ في $\cos^{3} (x)$ بجمع الأُسس.

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خطوة 1.2.6.53.1

انقُل $\cos^{3} (x)$ .

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

خطوة 1.2.6.53.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.53.3

أضف $3$ و $3$ .

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

خطوة 1.2.6.54

اضرب $- 120$ في $- 120$ .

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

خطوة 1.2.6.55

اضرب $\cos^{3} (x)$ في $\cos (x)$ بجمع الأُسس.

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خطوة 1.2.6.55.1

انقُل $\cos (x)$ .

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

خطوة 1.2.6.55.2

اضرب $\cos (x)$ في $\cos^{3} (x)$ .

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خطوة 1.2.6.55.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.55.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.55.3

أضف $1$ و $3$ .

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

خطوة 1.2.6.56

اضرب $9$ في $- 120$ .

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

خطوة 1.2.6.57

اضرب $\cos (x)$ في $\cos^{9} (x)$ بجمع الأُسس.

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خطوة 1.2.6.57.1

انقُل $\cos^{9} (x)$ .

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

خطوة 1.2.6.57.2

اضرب $\cos^{9} (x)$ في $\cos (x)$ .

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خطوة 1.2.6.57.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.57.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.57.3

أضف $9$ و $1$ .

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

خطوة 1.2.6.58

اضرب $256$ في $9$ .

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

خطوة 1.2.6.59

اضرب $\cos (x)$ في $\cos^{7} (x)$ بجمع الأُسس.

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خطوة 1.2.6.59.1

انقُل $\cos^{7} (x)$ .

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

خطوة 1.2.6.59.2

اضرب $\cos^{7} (x)$ في $\cos (x)$ .

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خطوة 1.2.6.59.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.59.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.59.3

أضف $7$ و $1$ .

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

خطوة 1.2.6.60

اضرب $- 576$ في $9$ .

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

خطوة 1.2.6.61

اضرب $\cos (x)$ في $\cos^{5} (x)$ بجمع الأُسس.

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خطوة 1.2.6.61.1

انقُل $\cos^{5} (x)$ .

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

خطوة 1.2.6.61.2

اضرب $\cos^{5} (x)$ في $\cos (x)$ .

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خطوة 1.2.6.61.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.61.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.61.3

أضف $5$ و $1$ .

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

خطوة 1.2.6.62

اضرب $432$ في $9$ .

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

خطوة 1.2.6.63

اضرب $\cos (x)$ في $\cos^{3} (x)$ بجمع الأُسس.

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خطوة 1.2.6.63.1

انقُل $\cos^{3} (x)$ .

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

خطوة 1.2.6.63.2

اضرب $\cos^{3} (x)$ في $\cos (x)$ .

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خطوة 1.2.6.63.2.1

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.63.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.63.3

أضف $3$ و $1$ .

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

خطوة 1.2.6.64

اضرب $- 120$ في $9$ .

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

خطوة 1.2.6.65

اضرب $9 \cos (x) (9 \cos (x))$ .

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خطوة 1.2.6.65.1

اضرب $9$ في $9$ .

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

خطوة 1.2.6.65.2

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.65.3

ارفع $\cos (x)$ إلى القوة $1$ .

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

خطوة 1.2.6.65.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 1.2.6.65.5

أضف $1$ و $1$ .

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

خطوة 1.2.7

اطرح $147456 \cos^{16} (x)$ من $- 147456 \cos^{16} (x)$ .

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

خطوة 1.2.8

أضف $110592 \cos^{14} (x)$ و $331776 \cos^{14} (x)$ .

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

خطوة 1.2.9

أضف $442368 \cos^{14} (x)$ و $110592 \cos^{14} (x)$ .

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

خطوة 1.2.10

اطرح $248832 \cos^{12} (x)$ من $- 30720 \cos^{12} (x)$ .

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

خطوة 1.2.11

اطرح $248832 \cos^{12} (x)$ من $- 279552 \cos^{12} (x)$ .

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

خطوة 1.2.12

اطرح $30720 \cos^{12} (x)$ من $- 528384 \cos^{12} (x)$ .

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

خطوة 1.2.13

أضف $2304 \cos^{10} (x)$ و $69120 \cos^{10} (x)$ .

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

خطوة 1.2.14

أضف $71424 \cos^{10} (x)$ و $186624 \cos^{10} (x)$ .

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

خطوة 1.2.15

أضف $258048 \cos^{10} (x)$ و $69120 \cos^{10} (x)$ .

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

خطوة 1.2.16

أضف $327168 \cos^{10} (x)$ و $2304 \cos^{10} (x)$ .

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

خطوة 1.2.17

اطرح $51840 \cos^{8} (x)$ من $- 5184 \cos^{8} (x)$ .

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

خطوة 1.2.18

اطرح $51840 \cos^{8} (x)$ من $- 57024 \cos^{8} (x)$ .

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

خطوة 1.2.19

اطرح $5184 \cos^{8} (x)$ من $- 108864 \cos^{8} (x)$ .

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

خطوة 1.2.20

أضف $3888 \cos^{6} (x)$ و $14400 \cos^{6} (x)$ .

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

خطوة 1.2.21

أضف $18288 \cos^{6} (x)$ و $3888 \cos^{6} (x)$ .

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

خطوة 1.2.22

اطرح $1080 \cos^{4} (x)$ من $- 1080 \cos^{4} (x)$ .

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

خطوة 1.2.23

طبّق خاصية التوزيع.

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

خطوة 1.2.24

بسّط.

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خطوة 1.2.24.1

اضرب $65536$ في $2$ .

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

خطوة 1.2.24.2

اضرب $- 294912$ في $2$ .

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

خطوة 1.2.24.3

اضرب $552960$ في $2$ .

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

خطوة 1.2.24.4

اضرب $- 559104$ في $2$ .

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

خطوة 1.2.24.5

اضرب $329472$ في $2$ .

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

خطوة 1.2.24.6

اضرب $- 114048$ في $2$ .

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

خطوة 1.2.24.7

اضرب $22176$ في $2$ .

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

خطوة 1.2.24.8

اضرب $- 2160$ في $2$ .

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

خطوة 1.2.24.9

اضرب $81$ في $2$ .

خطوة 2

جمّع الحدود المتعاكسة في $1 + 131072 \cos^{18} (x) - 589824 \cos^{16} (x) + 1105920 \cos^{14} (x) - 1118208 \cos^{12} (x) + 658944 \cos^{10} (x) - 228096 \cos^{8} (x) + 44352 \cos^{6} (x) - 4320 \cos^{4} (x) + 162 \cos^{2} (x) - 1$ .

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خطوة 2.1

اطرح $1$ من $1$ .

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

خطوة 2.2

أضف $0$ و $131072 \cos^{18} (x)$ .

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