Prove the Identity

 sin2x / [1-cos2x ]  =  cotx           work with the left side

sin 2x  /  [ 1 - (1 - 2sin ^2 x ) ]  

sin 2x / [ 2 sin^2 x ] [ 2sin x cosx] / [ 2 sin ^2 x ]

sin x cos x  / [ sin ^2 x]

sin x cos x / [ sin x * sin x ] =

cos x / sin x      =

cot x