How do you prove #1/(1-cosA) + 1/(1+cosA)= 2+2cot^2A#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer bp Apr 30, 2015 Starting with the LHS, the sum would be #(1+cos A +1 -cos A)/((1+cosA)(1-cosA))# =#2/(1-cos^2A)# = #2/sin^2A# =#2csc^2A# = #2(1+cot^2A)# =#2+2cot^2A# 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 5304 views around the world You can reuse this answer Creative Commons License