Prove (1 - cosX) / (1 + coxX) = (cscX - cotX)^2

to remove 1+ cos x from denominator multiply numerator and denominator by 1- cos x

= (1-cos x)^2/((1+ cos x)(1-cos x))
= (1- cos x)^2/ (1- cos^2 x)
= (1- cos x)^2/ sin ^2 x
= ((- cos x)/sin x)^2
= (csc x - cot x)^2