How do you verify the identity (1+tan^2theta)/(1-tan^2theta)=1/(2cos^2theta-1)? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Deepak G. Aug 7, 2016 L.H.S=R.H.S. Explanation: Since sin^2 theta+cos^2 theta=1 L.H.S.=(1+tan^2 theta)/(1-tan^2 theta) =(1+sin^2 theta/cos^2 theta)/(1-sin^2theta/cos^2 theta) =((cos^2 theta+sin^2 theta)/(cancelcos^2 theta))/((cos^2 theta-sin^2 theta)/(cancelcos^2theta) =(cos^2 theta+sin^2 theta)/(cos^2 theta-sin^2 theta) =1/(cos^2 theta-sin^2 theta) =1/(cos^2 theta-(1-cos^2 theta) =1/(cos^2 theta+cos^2 theta-1) =1/(2cos^2 theta-1) Hence L.H.S=R.H.S. 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 4197 views around the world You can reuse this answer Creative Commons License