化简 1/(cos^2(x))+1/(sin^2(x))

解答

化简

\frac{1}{cos ^{2} ( x )} + \frac{1}{sin ^{2} ( x )}

csc^{2} (x) sec^{2} (x)

求解步骤

\frac{1}{cos ^{2} ( x )} + \frac{1}{sin ^{2} ( x )}

使用基本三角恒等式:

\frac{1}{sin ( x )} = csc (x)

= \frac{1}{cos ^{2} ( x )} + csc^{2} (x)

用 sin, cos 表示

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

使用三角恒等式改写

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

f (a) = \frac{( 1 + sin ( a ) )}{( 1 - sin ( a ) )}

s im pl i f y \frac{sin ( x )}{sin ( \frac{x}{2} )}

s im pl i f y cos (x) 1 - sin (x)

f a c t or p^{2} + p^{8}

s im pl i f y 7 h^{2} + 2 h + 5 - h^{2} + h