How do you verify #(1-tan^2)/(1+tan^2)=cos^2 - sin^2#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Nghi N. May 25, 2015 #(1 - tan^2)/(1 + tan^2) = (cos^2 - sin^2)/(cos^2 + sin^2) (cos^2/cos^2)# = =#(cos^2 - sin^2)/1 = cos^2 - sin^2# 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 8515 views around the world You can reuse this answer Creative Commons License