How do you verify #cscx-1=cot^2x/(cscx+1)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Noah G Nov 12, 2016 #1/sinx - 1 = (cos^2x/sin^2x)/(1/sinx+ 1)# #1/sinx- sinx/sinx= (cos^2x/sin^2x)/((1 + sinx)/sinx)# #(1 - sinx)/sinx= cos^2x/sin^2x xx sinx/(1 + sinx)# #(1 - sinx)/sinx= (1 - sin^2x)/sinx xx 1/(1 + sinx)# #(1 - sinx)/sinx = ((1 + sinx)(1 - sinx))/sinx xx 1/(1 + sinx)# #(1- sinx)/sinx = (1 - sinx)/sinx# #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 6494 views around the world You can reuse this answer Creative Commons License