Prove that sin2x/1 + cos2x = tanx

Question

Prove that

\(\frac{sin\,2x}{1\,+\,cos2x}= tanx\)

sin2x/1 + cos2x = tanx

Answer 1

To Prove: \(\frac{sin2x}{1+cos2x}\) = tanx

Taking LHS,

= \(\frac{sinx}{cosx}\)

= tanx   [∵ tanθ = \(\frac{sin\theta}{cos\theta}\)]

= RHS

∴ LHS = RHS

Hence Proved