I am having trouble proving the following:
cscx + secx = cotx + tanx
sinx + cosx
$\displaystyle \frac {\csc x+\sec x}{\sin x+\cos x}=\frac {\frac 1{\sin x}+\frac 1{\cos x}}{\sin x+\cos x}=\frac {\frac {\cos x+\sin x}{\sin x\cos x}}{\sin x+\cos x}=\frac 1{\sin x\cos x}=\frac {\cos x}{\sin x}+\frac {\sin x}{\cos x}$
using the identity $\displaystyle \sin^2x+\cos^2x=1$ (in the last step).