How do you prove the identity (sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Mar 9, 2018 See Below Explanation: Use the Property : color(blue)(sin^2x+cos^2x=1 LHS : (sinx-cosx)/(sinx+cosx) =(sinx-cosx)/(sinx+cosx)* (sinx+cosx)/(sinx+cosx)-> multiply by conjugate =(sin^2x-cos^2x)/(sin^2x+2sinxcosx+cos^2x) =(sin^2x-[1-sin^2x])/([sin^2x+cos^2x]+2sinxcosx) =(sin^2x-1+sin^2x)/(1+2sinxcosx) =(2sin^2x-1)/(1+2sinxcosx) =RHS 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 tan^2x/(secx+1)= (1-cosx)/cosx? See all questions in Proving Identities Impact of this question 57795 views around the world You can reuse this answer Creative Commons License