Can you please help me prove that ((1-cosx)/(1+cosx))=(cscx-cotx)^2?

Question

I can only do work on one side to prove that its end result is equal to the other side.

Answer 1

LS = (1-cosx)/(1+cosx)
= (1-cosx)/(1+cosx) * (1-cosx)/(1-cosx)
= (1-cosx)^2 /(1 - cos^2 x)
= (1-cosx)^2 /sin^2 x
= ( (1-cosx)/sinx )^2
= (1/sinx - cosx/sinx)^2
= (cscx - cotx)^2
= RS