Question

Prove the identity: sin 2x/(1 + cos 2x) = tan x

Answer 1

Let us consider the LHS

sin 2x/(1 + cos 2x)

As we know that cos 2x = 1 – 2 sin² x

= 2 cos² x – 1

Sin 2x = 2 sin x cos x

Therefore,

sin 2x/(1 + cos 2x) = [2 sin x cos x/(1 + (2cos²x – 1))]

= [2 sin x cos x/(1 + 2cos² x – 1)]

= [2 sin x cos x/2 cos² x]

= sin x/cos x

= tan x

= RHS

Thus proved.