Verify that (cos^2x - sin^2x) / (1-tan^2x) = cos^2x ? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Nov 12, 2016 see below Explanation: #(cos^2x-sin^2x)/(1-tan^2x) = cos^2x# Left Side:#=(cos^2x-sin^2x)/(1-tan^2x) # #=(cos^2x-sin^2x)/(1-sin^2x/cos^2x) # #=(cos^2x-sin^2x)/((cos^2x-sin^2x)/cos^2x) # #=cancel(cos^2x-sin^2x) cos^2x/cancel(cos^2x-sin^2x) # #=cos^2x# #:.=#Right Side 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 33867 views around the world You can reuse this answer Creative Commons License