Tan(x+pi/4)=1+2sinx cosx/1-2sin^2 x prove? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Shwetank Mauria 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) Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove \csc \theta \times \tan \theta = \sec \theta? How do you prove (1-\cos^2 x)(1+\cot^2 x) = 1? How do you show that 2 \sin x \cos x = \sin 2x? is true for (5pi)/6? How do you prove that sec xcot x = csc x? How do you prove that cos 2x(1 + tan 2x) = 1? How do you prove that (2sinx)/[secx(cos4x-sin4x)]=tan2x? How do you verify the identity: -cotx =(sin3x+sinx)/(cos3x-cosx)? How do you prove that (tanx+cosx)/(1+sinx)=secx? How do you prove the identity (sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)? See all questions in Proving Identities Impact of this question 3866 views around the world You can reuse this answer Creative Commons License