展開する (cos(a)-2sin(b))^2

解

展開する

(cos (a) - 2 sin (b))^{2}

cos^{2} (a) - 4 cos (a) sin (b) + 4 sin^{2} (b)

解答ステップ

(cos (a) - 2 sin (b))^{2}

完全平方式を適用する:

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

(cos (a) - 2 sin (b))^{2} = cos^{2} (a) - 2 cos (a) \cdot 2 sin (b) + (2 sin (b))^{2}

= cos^{2} (a) - 2 cos (a) \cdot 2 sin (b) + (2 sin (b))^{2}

簡素化

cos^{2} (a) - 2 cos (a) \cdot 2 sin (b) + (2 sin (b))^{2} : cos^{2} (a) - 4 cos (a) sin (b) + 4 sin^{2} (b)

= cos^{2} (a) - 4 cos (a) sin (b) + 4 sin^{2} (b)