Prove that (1-2sin^2x)/(1+sin2x) = (1-tanx)/(1+tanx)?

1 Answer
Apr 10, 2016

Please see below.

Explanation:

To prove (1-2sin^2x)/(1+sin2x) = (1-tanx)/(1+tanx), let us start from left hand side.

(1-2sin^2x)/(1+sin2x) is equivalent to

(1-sin^2x-sin^2x)/(cos^2x+sin^2x+2sinxcosx)

= (cos^2x-sin^2x)/(cosx+sinx)^2

= ((cosx+sinx)(cosx-sinx))/(cosx+sinx)^2

= (cosx-sinx)/(cosx+sinx)

Now dividing numerator and denominator by cosx

= (1-sinx/cosx)/(1+sinx/cosx)

= (1-tanx)/(1+tanx)