Trignometry

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

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

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  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

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