How do you verify the identity #1/(csctheta+1)+1/(csctheta-1)=2sec^2thetasintheta#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Cesareo R. Sep 9, 2016 See below. Explanation: #1/(csctheta+1)+1/(csctheta-1)=2sec^2thetasintheta# #1/(csctheta+1)+1/(csctheta-1)=2csctheta/(csc^2theta-1)=# #=2(sin^2 theta csc theta) /cos^2theta = 2sin^2theta sec^2theta/sintheta = 2sin theta sec^2theta# 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 3036 views around the world You can reuse this answer Creative Commons License