How do you prove that #(1 + tan^2x)/(1 + cot^2x) = ((1 - tanx)/(1 - cotx))^2#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Noah G May 1, 2017 #(1 + sin^2x/cos^2x)/(1 + cos^2x/sin^2x) = ((1 - sinx/cosx)/(1 - cosx/sinx))^2# #((cos^2x + sin^2x)/cos^2x)/((sin^2x + cos^2x)/sin^2x) = (((cosx - sinx)/cosx)/((sinx - cosx)/sinx))^2# #sin^2x/cos^2x = (-sinx/cosx)^2# #sin^2x/cos^2x= sin^2x/cos^2x# Hopefully this helps! 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 9967 views around the world You can reuse this answer Creative Commons License