How do you prove the identity #(csc theta - 1) / cot theta = cot theta / (csc theta + 1)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer dani83 Aug 19, 2015 # sin^2 A + cos^2 A = 1 # # 1 + cot^2 A = csc^2 A # # (csc theta - 1)/cot theta = ((csc theta - 1)(csc theta + 1))/(cot theta (csc theta + 1)) = (csc^2 theta - 1)/(cot theta (csc theta + 1)) = cot theta/(csc theta + 1) # 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 10213 views around the world You can reuse this answer Creative Commons License