Question #b092d Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Noah G May 9, 2016 #(1 + tanx)/(1 + cotx) = (1 - tanx)/(cotx - 1)# #(1 + (sinx/cosx))/(1 + (cosx/sinx)) = (1 - (sinx/cosx))/((cosx/sinx) - 1)# #((cosx + sinx)/cosx)/((sinx + cosx)/sinx) = ((cosx - sinx)/cosx)/((cosx - sinx)/sinx)# #sinx/cosx = sinx/cosx# Identity proved!! 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 2209 views around the world You can reuse this answer Creative Commons License