展開する (cos^2(x)+sin^2(x))^2

解

展開する

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

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

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

(cos^{2} (x))^{2} + 2 cos^{2} (x) sin^{2} (x) + (sin^{2} (x))^{2} : cos^{4} (x) + 2 sin^{2} (x) - sin^{4} (x)

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