Question

Prove the identity.

2tanx/1+tan^2x=sin^2x

Answer 1

Not so.
if x=pi/4,

2*1/(1+1) = 1
sin^2 pi/4 = 1/2

I think you mean

2tanx/(1+tan^2x)=sin2x
since
2sinx/cosx / sec^2x
2sinx/cosx * cos^2x
2sinx*cosx = sin2x

If I garbled it, make the corrections and repost if needed.