How do you verify #(1-tan^2x) / (1+tan^2x) = 1-2sin^2#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Deepak G. Jul 24, 2016 #L.H.S=R.H.S# Explanation: #L.H.S = (1-tan^2x)/(1+tan^2x)# #=(1-sin^2x/cos^2x)/(1+sin^2x/cos^2x# #=((cos^2x-sin^2x)/cos^2x)/((cos^2x+sin^2x)/cos^2x)# #=(cos^2x-sin^2x)/(cos^2x+sin^2x)# #=(cos^2x-sin^2x)/1 ; Since cos^2x+sin^2x=1;cos^2x=1-sin^2x# #=cos^2x-sin^2x# #=1-sin^2x-sin^2x# #=1-2sin^2x# #=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 34604 views around the world You can reuse this answer Creative Commons License