How do you prove tan2x + sec2x = (cosx + sinx) / (cosx – sinx)? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Jul 1, 2016 As below Explanation: RHS = (cosx + sinx) / (cosx – sinx) =( (cosx + sinx) (cosx +sinx) )/( (cosx - sinx) (cosx +sinx)) = (cosx + sinx) ^2/ (cos^2x – sin^2x) = (cos^2x + sin^2x+2sinxcosx) / (cos2x) =(1+sin2x)/(cos2x)=1/(cos2x)+(sin2x)/(cos2x) =tan2x+sec2x=LHS proved 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 14866 views around the world You can reuse this answer Creative Commons License