展開する (2-2cos(x))^2

解

展開する

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

4 - 8 cos (x) + 4 cos^{2} (x)

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

2^{2} - 2 \cdot 2 \cdot 2 cos (x) + (2 cos (x))^{2} : 4 - 8 cos (x) + 4 cos^{2} (x)

= 4 - 8 cos (x) + 4 cos^{2} (x)