因数 tan^4(x)-sec^4(x)

解

因数

tan^{4} (x) - sec^{4} (x)

(tan^{2} (x) + sec^{2} (x)) (tan (x) + sec (x)) (tan (x) - sec (x))

解答ステップ

tan^{4} (x) - sec^{4} (x)

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

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

= (tan^{2} (x))^{2} - (sec^{2} (x))^{2}

2乗の差の公式を適用する:

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

(tan^{2} (x))^{2} - (sec^{2} (x))^{2} = (tan^{2} (x) + sec^{2} (x)) (tan^{2} (x) - sec^{2} (x))

= (tan^{2} (x) + sec^{2} (x)) (tan^{2} (x) - sec^{2} (x))

因数

tan^{2} (x) - sec^{2} (x) : (tan (x) + sec (x)) (tan (x) - sec (x))

= (tan^{2} (x) + sec^{2} (x)) (tan (x) + sec (x)) (tan (x) - sec (x))