展開する (cos(x)-xsin(x))^2

解

展開する

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

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

解答ステップ

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

完全平方式を適用する:

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

(cos (x) - x sin (x))^{2} = cos^{2} (x) - 2 cos (x) x sin (x) + (x sin (x))^{2}

= cos^{2} (x) - 2 cos (x) x sin (x) + (x sin (x))^{2}

簡素化

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

= x^{2} sin^{2} (x) - x sin (2 x) + cos^{2} (x)