How do you verify #cosx/(1-sinx)= secx+tanx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer dani83 Aug 20, 2015 # sec A = 1/cos A# #tan A = sin A/cos A# # sin^2 A + cos^2 A = 1# # sec x + tan x = (1+sin x)/cos x = ((1+sin x)(1-sin x))/(cos x(1-sin x)) = (1-sin^2 x)/(cos x(1-sin x)) = cos x/(1-sin x) # 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 39585 views around the world You can reuse this answer Creative Commons License