I need to verify this identity:

(tan x/(1 + cos x)) + (sin x/(1 - cos x)) = cot x + (sec s)(csc x)

I've tried it twice now, and on the left side I keep getting:

sin^2 x /(cot x + (sec x)(csc x)

What I'm doing is multiplying the denominator and the numerator of the first fraction by (1 - cos x) to get sin x^2 on the bottom, and doing the same with the second fraction by multiplying by (1 + cos x). Simplifying that give me the right half of the identity under sin ^2 X

It's supposed to be an identity but I guess I'm screwing it up... can someone try it out and post their work so I can see what I'm doing wrong?

I'd very much appreciate it.