How do you prove #cot^2 x/ (1+csc x) = (1-sin x)/ sin x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Kalyanam S. Jul 8, 2018 As proved below. Explanation: #cot^2 x = csc^2 x - 1, csc x = 1/ sin x# #cot^2 x / (1 + csc x) = (csc^2 x - 1) / (csc x + 1)# #=> (cancel(csc x + 1) (csc x - 1)) / cancel(csc x + 1)# #=> csc x - 1 = (1/sin x - 1) color(violet)(= (1-sin x) / sin x# 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 21768 views around the world You can reuse this answer Creative Commons License