1.

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

Answer»

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.



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