因式分解 tan^4(x)-sec^4(x)

解答

因式分解

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

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

求解步骤

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}

使用平方差公式:

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))

因式分解

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))

s im pl i f y \frac{4}{3} (2)

s im pl i f y \frac{1}{7} \cdot \frac{5}{2}

s im pl i f y \frac{24 x ^{2} + 4 x}{4 x}

f a c t or x^{6} - x^{3}

s im pl i f y 3051 (3)^{6}