Question #9925d Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Noah G Jan 10, 2017 #(sinx/cosx - 1)/(sinx/cosx + 1) = (1 - cosx/sinx)/(1 + cosx/sinx)# #((sinx - cosx)/cosx)/((sinx + cosx)/cosx) = ((sinx - cosx)/sinx)/((sinx + cosx)/sinx)# #(sinx - cosx)/cosx * cosx/(sinx + cosx) = (sinx - cosx)/sinx * sinx/(sinx + cosx)# #(sinx - cosx)/(sinx + cosx) = (sinx - cosx)/(sinx + cosx)# #LHS = RHS# 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 2836 views around the world You can reuse this answer Creative Commons License