Tan(x+pi/4)=1+2sinx cosx/1-2sin^2 x prove?

1 Answer
Jul 7, 2017

Please see below.

Explanation:

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

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

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

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

= (cosx+sinx)/(cosx-sinx) - dividing each term by cosx

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

= (tan(pi/4)+tanx)/(1-tan(pi/4)tanx)

= tan(pi/4+x)