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

Answer 1

I assume you meant
tan^2x/(1 + tan^2x)

LS = tan^2x/(1 + sec^2x - 1)
= tan^2x/sec^2
= (sin^2x/cos^2x) (cos^2x)
= sin^2 x
= RS