tanx/(1 + cosx) + sinx/(1 - cosx) = cotx + secxcscx
HELPO!!!
Move from LHS to RHS:
$\displaystyle \begin{aligned}\frac{\tan x}{1+\cos x}+\frac{\sin x}{1-\cos x}&=\frac{\tan x(1-\cos x)}{1-\cos^2x}+\frac{\sin x(1+\cos x)}{1-\cos^2x}\\&=\frac{(\tan x-\sin x)+(\sin x +\sin x\cos x)}{1-\cos^2x}\end{aligned}$
Can you finish this? If you can't, see the spoiler for the next hint.
Spoiler: