How do you simplify #cos x /( sec x -1) + cos x / (sec x +1)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Jul 8, 2016 #2cot^2x# Explanation: #cosx/(secx-1)+ cosx/(secx+1)# #=cosx(1/(secx-1)+ 1/(secx+1))# #=cosx((secx+1+secx-1)/((secx-1)(secx+1)))# #=(cosx*2secx)/(sec^2x-1)# #=2/tan^2x=2cot^2x# 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 9858 views around the world You can reuse this answer Creative Commons License