展開する (1-cos^2(x))^3

解

展開する

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

1 - 3 cos^{2} (x) + 3 cos^{4} (x) - cos^{6} (x)

解答ステップ

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

完全立方式を適用する:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

簡素化

1^{3} - 3 \cdot 1^{2} cos^{2} (x) + 3 \cdot 1 \cdot (cos^{2} (x))^{2} - (cos^{2} (x))^{3} : 1 - 3 cos^{2} (x) + 3 cos^{4} (x) - cos^{6} (x)

= 1 - 3 cos^{2} (x) + 3 cos^{4} (x) - cos^{6} (x)