Question

Prove the identity: sin 2x/(1 – cos 2x) = cot x

Answer 1

Let us consider the LHS

sin 2x/(1 – cos 2x)

As we know that cos 2x = 1 – 2 sin² x

Sin 2x = 2 sin x cos x

Therefore,

sin 2x/(1 – cos 2x) = (2 sin x cos x)/(1 – (1 – 2sin² x))

= (2 sin x cos x)/(1 – 1 + 2sin² x)]

= [2 sin x cos x/2 sin² x]

= cos x/sin x

= cot x

= RHS

Thus proved.