How to prove (1+2sinx.cosx)/(1-2sin^2x)=(1+tanx)/(1-tan)

Question

(1+2sinx.cosx)/(1-2sin^2)=(1+tanx)/(1-tanx)

Answer 1

How to prove (1+2sinx.cosx)/(1-2sin^2x)=(1+tanx)/(1-tan)

Write the rhs as (1+tanx)/(1-tan) = (cosx + sinx) / (cosx - sinx)

Write the numerator of the lhs as (1+2sinx.cosx) = cos^2x + sin^2x + 2sinx.cosx = (cosx + sinx)^2

Write the denominator of the lhs as (1 - 2sin^2x) = cos^2x - sin^2x = (cosx + sinx)(cosx - sinx)

The lhs now equals (cosx + sinx)^2​ / [(cosx + sinx)(cosx - sinx)] = (cosx + sinx)​ / (cosx - sinx) = rhs

​Ans: rhs = lhs