展開する (sin(x)+xcos(x))^2

解

展開する

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

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

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

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

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