삼각법 예제

{cos}^{2} (3 x) - {sin}^{2} (3 x)

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

단계 1

두 항 모두 완전제곱식이므로, 제곱의 차 공식

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ 을 이용하여 인수분해합니다. 이 때

a = cos (3 x)

$a = \cos (3 x)$ 이고

b = sin (3 x)

$b = \sin (3 x)$ 입니다.

(cos (3 x) + sin (3 x)) (cos (3 x) - sin (3 x))

$(\cos (3 x) + \sin (3 x)) (\cos (3 x) - \sin (3 x))$

단계 2

항을 간단히 합니다.

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단계 2.1

각 항을 간단히 합니다.

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단계 2.1.1

삼배각 공식을 사용하여

cos (3 x)

$\cos (3 x)$ 를

4 {cos}^{3} (x) - 3 cos (x)

$4 \cos^{3} (x) - 3 \cos (x)$ 로 바꿉니다.

(4 {cos}^{3} (x) - 3 cos (x) + sin (3 x)) (cos (3 x) - sin (3 x))

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

단계 2.1.2

사인 세배각 공식을 적용합니다.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (cos (3 x) - sin (3 x))

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

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (cos (3 x) - sin (3 x))

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

단계 2.2

각 항을 간단히 합니다.

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단계 2.2.1

삼배각 공식을 사용하여

cos (3 x)

$\cos (3 x)$ 를

4 {cos}^{3} (x) - 3 cos (x)

$4 \cos^{3} (x) - 3 \cos (x)$ 로 바꿉니다.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) - sin (3 x))

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

단계 2.2.2

사인 세배각 공식을 적용합니다.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) - (- 4 {sin}^{3} (x) + 3 sin (x)))

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

단계 2.2.3

분배 법칙을 적용합니다.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) - (- 4 {sin}^{3} (x)) - (3 sin (x)))

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

단계 2.2.4

- 4

$- 4$ 에

- 1

$- 1$ 을 곱합니다.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - (3 sin (x)))

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

단계 2.2.5

3

$3$ 에

- 1

$- 1$ 을 곱합니다.

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

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

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

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

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

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

단계 3

첫 번째 수식의 항과 두 번째 수식의 항을 각각 곱하여

(4 {cos}^{3} (x) - 3 cos (x) - 4 {sin}^{3} (x) + 3 sin (x)) (4 {cos}^{3} (x) - 3 cos (x) + 4 {sin}^{3} (x) - 3 sin (x))

$(4 \cos^{3} (x) - 3 \cos (x) - 4 \sin^{3} (x) + 3 \sin (x)) (4 \cos^{3} (x) - 3 \cos (x) + 4 \sin^{3} (x) - 3 \sin (x))$ 를 전개합니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 {cos}^{3} (x) (4 {sin}^{3} (x)) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (4 {cos}^{3} (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (4 {cos}^{3} (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

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

단계 4

항을 간단히 합니다.

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단계 4.1

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 {cos}^{3} (x) (4 {sin}^{3} (x)) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (4 {cos}^{3} (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (4 {cos}^{3} (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

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단계 4.1.1

인수가 항

4 {cos}^{3} (x) (4 {sin}^{3} (x))

$4 \cos^{3} (x) (4 \sin^{3} (x))$ 과(와)

- 4 {sin}^{3} (x) (4 {cos}^{3} (x))

$- 4 \sin^{3} (x) (4 \cos^{3} (x))$ (으)로 표현되도록 다시 정렬합니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 \cdot 4 {cos}^{3} (x) {sin}^{3} (x) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 \cdot 4 {cos}^{3} (x) {sin}^{3} (x) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (4 {cos}^{3} (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) + 4 \cdot 4 \cos^{3} (x) \sin^{3} (x) + 4 \cos^{3} (x) (- 3 \sin (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \cdot 4 \cos^{3} (x) \sin^{3} (x) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (4 \cos^{3} (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.1.2

4 \cdot 4 {cos}^{3} (x) {sin}^{3} (x)

$4 \cdot 4 \cos^{3} (x) \sin^{3} (x)$ 에서

4 \cdot 4 {cos}^{3} (x) {sin}^{3} (x)

$4 \cdot 4 \cos^{3} (x) \sin^{3} (x)$ 을 뺍니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) + 0 - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (4 {cos}^{3} (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) + 4 \cos^{3} (x) (- 3 \sin (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) + 0 - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (4 \cos^{3} (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.1.3

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x))

0

$0$ 에 더합니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) + 4 {cos}^{3} (x) (- 3 sin (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (4 {cos}^{3} (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

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

단계 4.1.4

인수가 항

4 {cos}^{3} (x) (- 3 sin (x))

$4 \cos^{3} (x) (- 3 \sin (x))$ 과(와)

3 sin (x) (4 {cos}^{3} (x))

$3 \sin (x) (4 \cos^{3} (x))$ (으)로 표현되도록 다시 정렬합니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) - 3 \cdot 4 {cos}^{3} (x) sin (x) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 \cdot 4 {cos}^{3} (x) sin (x) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cdot 4 \cos^{3} (x) \sin (x) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \cdot 4 \cos^{3} (x) \sin (x) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.1.5

- 3 \cdot 4 {cos}^{3} (x) sin (x)

$- 3 \cdot 4 \cos^{3} (x) \sin (x)$ 를

3 \cdot 4 {cos}^{3} (x) sin (x)

$3 \cdot 4 \cos^{3} (x) \sin (x)$ 에 더합니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 0 + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

$4 \cos^{3} (x) (4 \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 0 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.1.6

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x))

0

$0$ 에 더합니다.

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

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

4 {cos}^{3} (x) (4 {cos}^{3} (x)) + 4 {cos}^{3} (x) (- 3 cos (x)) - 3 cos (x) (4 {cos}^{3} (x)) - 3 cos (x) (- 3 cos (x)) - 3 cos (x) (4 {sin}^{3} (x)) - 3 cos (x) (- 3 sin (x)) - 4 {sin}^{3} (x) (- 3 cos (x)) - 4 {sin}^{3} (x) (4 {sin}^{3} (x)) - 4 {sin}^{3} (x) (- 3 sin (x)) + 3 sin (x) (- 3 cos (x)) + 3 sin (x) (4 {sin}^{3} (x)) + 3 sin (x) (- 3 sin (x))

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

단계 4.2

각 항을 간단히 합니다.

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단계 4.2.1

곱셈의 교환법칙을 사용하여 다시 씁니다.

$4 \cdot 4 \cos^{3} (x) \cos^{3} (x) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.2

지수를 더하여

$\cos^{3} (x)$ 에

$\cos^{3} (x)$ 을 곱합니다.

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단계 4.2.2.1

$\cos^{3} (x)$ 를 옮깁니다.

$4 \cdot 4 (\cos^{3} (x) \cos^{3} (x)) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.2.2

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

$4 \cdot 4 {\cos (x)}^{3 + 3} + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.2.3

$3$ 를

$3$ 에 더합니다.

$4 \cdot 4 \cos^{6} (x) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.3

$4$ 에

$4$ 을 곱합니다.

$16 \cos^{6} (x) + 4 \cos^{3} (x) (- 3 \cos (x)) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.4

지수를 더하여

$\cos^{3} (x)$ 에

$\cos (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.4.1

$\cos (x)$ 를 옮깁니다.

$16 \cos^{6} (x) + 4 (\cos (x) \cos^{3} (x)) \cdot - 3 - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.4.2

$\cos (x)$ 에

$\cos^{3} (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.4.2.1

$\cos (x)$ 를

$1$ 승 합니다.

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

단계 4.2.4.2.2

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

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

단계 4.2.4.3

$1$ 를

$3$ 에 더합니다.

$16 \cos^{6} (x) + 4 \cos^{4} (x) \cdot - 3 - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.5

$- 3$ 에

$4$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 \cos (x) (4 \cos^{3} (x)) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.6

지수를 더하여

$\cos (x)$ 에

$\cos^{3} (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.6.1

$\cos^{3} (x)$ 를 옮깁니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 (\cos^{3} (x) \cos (x)) \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.6.2

$\cos^{3} (x)$ 에

$\cos (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.6.2.1

$\cos (x)$ 를

$1$ 승 합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 (\cos^{3} (x) \cos^{1} (x)) \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.6.2.2

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 {\cos (x)}^{3 + 1} \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.6.3

$3$ 를

$1$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 3 \cos^{4} (x) \cdot 4 - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.7

$4$ 에

$- 3$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) - 3 \cos (x) (- 3 \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.8

$- 3 \cos (x) (- 3 \cos (x))$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.8.1

$- 3$ 에

$- 3$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos (x) \cos (x) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.8.2

$\cos (x)$ 를

$1$ 승 합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 (\cos^{1} (x) \cos (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.8.3

$\cos (x)$ 를

$1$ 승 합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 (\cos^{1} (x) \cos^{1} (x)) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.8.4

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 {\cos (x)}^{1 + 1} - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.8.5

$1$ 를

$1$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 3 \cos (x) (4 \sin^{3} (x)) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.9

$4$ 에

$- 3$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) - 3 \cos (x) (- 3 \sin (x)) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.10

$- 3$ 에

$- 3$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) - 4 \sin^{3} (x) (- 3 \cos (x)) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.11

$- 3$ 에

$- 4$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \sin^{3} (x) (4 \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.12

곱셈의 교환법칙을 사용하여 다시 씁니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 \sin^{3} (x) \sin^{3} (x) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.13

지수를 더하여

$\sin^{3} (x)$ 에

$\sin^{3} (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.13.1

$\sin^{3} (x)$ 를 옮깁니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 (\sin^{3} (x) \sin^{3} (x)) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.13.2

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 {\sin (x)}^{3 + 3} - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.13.3

$3$ 를

$3$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 4 \cdot 4 \sin^{6} (x) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.14

$- 4$ 에

$4$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 \sin^{3} (x) (- 3 \sin (x)) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.15

지수를 더하여

$\sin^{3} (x)$ 에

$\sin (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.15.1

$\sin (x)$ 를 옮깁니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 (\sin (x) \sin^{3} (x)) \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.15.2

$\sin (x)$ 에

$\sin^{3} (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.15.2.1

$\sin (x)$ 를

$1$ 승 합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 (\sin^{1} (x) \sin^{3} (x)) \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.15.2.2

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 {\sin (x)}^{1 + 3} \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.15.3

$1$ 를

$3$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) - 4 \sin^{4} (x) \cdot - 3 + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.16

$- 3$ 에

$- 4$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 3 \sin (x) (- 3 \cos (x)) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.17

$- 3$ 에

$3$ 을 곱합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 \sin (x) (4 \sin^{3} (x)) + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.18

지수를 더하여

$\sin (x)$ 에

$\sin^{3} (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.18.1

$\sin^{3} (x)$ 를 옮깁니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 (\sin^{3} (x) \sin (x)) \cdot 4 + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.18.2

$\sin^{3} (x)$ 에

$\sin (x)$ 을 곱합니다.

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.2.18.2.1

$\sin (x)$ 를

$1$ 승 합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 (\sin^{3} (x) \sin^{1} (x)) \cdot 4 + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.18.2.2

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 3 {\sin (x)}^{3 + 1} \cdot 4 + 3 \sin (x) (- 3 \sin (x))$

단계 4.2.18.3

$3$ 를

$1$ 에 더합니다.

단계 4.2.19

$4$ 에

$3$ 을 곱합니다.

단계 4.2.20

$3 \sin (x) (- 3 \sin (x))$ 을 곱합니다.

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단계 4.2.20.1

$- 3$ 에

$3$ 을 곱합니다.

단계 4.2.20.2

$\sin (x)$ 를

$1$ 승 합니다.

단계 4.2.20.3

$\sin (x)$ 를

$1$ 승 합니다.

단계 4.2.20.4

지수 법칙

$a^{m} a^{n} = a^{m + n}$ 을 이용하여 지수를 합칩니다.

단계 4.2.20.5

$1$ 를

$1$ 에 더합니다.

단계 4.3

항을 더해 식을 간단히 합니다.

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단계 4.3.1

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \cos (x) \sin^{3} (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$ 의 반대 항을 묶습니다.

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단계 4.3.1.1

인수가 항

$- 12 \cos (x) \sin^{3} (x)$ 과(와)

$12 \sin^{3} (x) \cos (x)$ (으)로 표현되도록 다시 정렬합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 12 \sin^{3} (x) \cos (x) + 9 \cos (x) \sin (x) + 12 \sin^{3} (x) \cos (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.1.2

$- 12 \sin^{3} (x) \cos (x)$ 를

$12 \sin^{3} (x) \cos (x)$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x) + 0 - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.1.3

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x)$ 를

$0$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \sin (x) \cos (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.1.4

인수가 항

$9 \cos (x) \sin (x)$ 과(와)

$- 9 \sin (x) \cos (x)$ (으)로 표현되도록 다시 정렬합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 9 \cos (x) \sin (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) - 9 \cos (x) \sin (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.1.5

$9 \cos (x) \sin (x)$ 에서

$9 \cos (x) \sin (x)$ 을 뺍니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) + 0 - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.1.6

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x)$ 를

$0$ 에 더합니다.

$16 \cos^{6} (x) - 12 \cos^{4} (x) - 12 \cos^{4} (x) + 9 \cos^{2} (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.2

$- 12 \cos^{4} (x)$ 에서

$12 \cos^{4} (x)$ 을 뺍니다.

$16 \cos^{6} (x) - 24 \cos^{4} (x) + 9 \cos^{2} (x) - 16 \sin^{6} (x) + 12 \sin^{4} (x) + 12 \sin^{4} (x) - 9 \sin^{2} (x)$

단계 4.3.3

$12 \sin^{4} (x)$ 를

$12 \sin^{4} (x)$ 에 더합니다.

$16 \cos^{6} (x) - 24 \cos^{4} (x) + 9 \cos^{2} (x) - 16 \sin^{6} (x) + 24 \sin^{4} (x) - 9 \sin^{2} (x)$