化简 (cos^4(x)-sin^4(x))/(cos^2(x)-sin^2(x))

解答

化简

\frac{cos ^{4} ( x ) - sin ^{4} ( x )}{cos ^{2} ( x ) - sin ^{2} ( x )}

1

求解步骤

\frac{cos ^{4} ( x ) - sin ^{4} ( x )}{cos ^{2} ( x ) - sin ^{2} ( x )}

因式分解

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

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

约分:

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

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

使用毕达哥拉斯恒等式:

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

= 1

s im pl i f y (\frac{( 3 + 2 ) a}{3})^{2}

s im pl i f y (1 + a)^{2} (1 + b^{2}) - (1 + b)^{2} (1 + a^{2})

s im pl i f y (\frac{1}{2})^{- 2 t}

s im pl i f y \frac{5}{x ^{2}} - x - 12 + \frac{3}{x ^{2}} - 16

f a c t or 3 x y + 11 x^{3} y