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 3647 views around the world You can reuse this answer Creative Commons License