因数 sin^4(x)-1

解

因数

sin^{4} (x) - 1

(sin^{2} (x) + 1) (sin (x) + 1) (sin (x) - 1)

解答ステップ

sin^{4} (x) - 1

sin^{4} (x) = (sin^{2} (x))^{2}

1 = 1^{2}

= (sin^{2} (x))^{2} - 1^{2}

2乗の差の公式を適用する:

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

(sin^{2} (x))^{2} - 1^{2} = (sin^{2} (x) + 1) (sin^{2} (x) - 1)

= (sin^{2} (x) + 1) (sin^{2} (x) - 1)

因数

sin^{2} (x) - 1 : (sin (x) + 1) (sin (x) - 1)

= (sin^{2} (x) + 1) (sin (x) + 1) (sin (x) - 1)