Question #0e37b Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Jul 5, 2017 #LHS=(1+cotX)/tanX-cotX# #=1/tanX+cotX/tanX-cotX# #=cotX+cotX/(1/cotX)-cotX# #=cotX/(1/cotX)# #=cot^2X# #=csc^2X-1# #=1/sin^2X-1# #=(1/cos^2X)/(sin^2X/cos^2X)-1# #=sec^2X/tan^2X-1=RHS# 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 934 views around the world You can reuse this answer Creative Commons License