Prove this identity:

[ (cos x) / (1 - tan x) ] + [ (sin x) / (1 - cot x) ] = cos x + sin x

So far I was able to put everything in terms of sin x and cos x

I understand that you have to multiply each dominator and numerator to get the common dominator.

Anyway, I got to this portion of it:

[ (cos^2 x) / (cos - sin) ] + [ (sin^2 x) / (sin - cos) ] = cos x + sin x

I do have a solution I could copy, but I'd rather understand how to do the problem. It's quite frustrating.