簡約 (1-cos(2x))^3

解

簡約

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

8 sin^{6} (x)

解答ステップ

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

簡素化

1 - cos (2 x) : 2 sin^{2} (x)

= (2 sin^{2} (x))^{3}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(2 sin^{2} (x))^{3} = 2^{3} (sin^{2} (x))^{3}

= 2^{3} (sin^{2} (x))^{3}

2^{3} = 8

= 8 (sin^{2} (x))^{3}

指数の規則を適用する:

(a^{b})^{c} = a^{b c},

, 以下を想定

a \geq 0

(sin^{2} (x))^{3} = sin^{2 \cdot 3} (x)

= 8 sin^{2 \cdot 3} (x)

数を乗じる:

2 \cdot 3 = 6

= 8 sin^{6} (x)