Prove that (cscx - cotx)^2 = (1-cosx)/(1+cosx)

[Random-Hero-]

Homework Statement

I can't seem to figure out how to prove that (cscx - cotx)^2 = (1-cosx)/(1+cosx).

Homework Equations

I believe I just need to do appropriate substitution using compound angle formulas, double angle formulas, etc...

The Attempt at a Solution

I got as far as this

1 + cot^2x - 2(1/tanx)(1/sinx) + cot^2x = (1-cosx)/(1+cosx)

Can anyone help me figure this out? Thanks in advance!

 

[Dick]

It's not that complicated. Turn everything into sin's and cos's. The denominator is sin(x)^2. That's (1-cos^2(x)). Factor it.