I'm not sure if what I did was right, so please verify it.

sin 2x/(1-cos 2x)=2 csc 2x-tan x

This is what I did:

LS= sin 2x/(1-cos2x)

= (2sinx cosx)/(1-(cos^2 x-sin^2 x))

= (2sinx cosx)/(cos^2 x+sin^2 x-cos^2 x+sin^2 x)

= (2 sin x cos x)/(2sin^2 x)

= cot x

RS= 2/(2sinx cosx)-sinx/cosx

= (2-2sin^2 x)/(2sinx cosx)

= (1-sin^2 x)/(sinx cosx)

= (1-(1-cos^2 x))/(sinx cosx)

= cos^2 x/(sinx cosx)

= cot x