因数 cos^3(x)-sin^3(x)

解

因数

cos^{3} (x) - sin^{3} (x)

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

解答ステップ

cos^{3} (x) - sin^{3} (x)

立方数の差の公式を適用する:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

cos^{3} (x) - sin^{3} (x) = (cos (x) - sin (x)) (cos^{2} (x) + sin (x) cos (x) + sin^{2} (x))

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