How do you solve #Cos x / (1- sin x) = sec x + tan x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Richard Jul 17, 2016 #(cosx)/(1-sinx) *(cosx)/cosx# #=(cos^2x)/((1-sinx)cosx)# #=(sin^2x-1)/((1-sinx)cosx)# #=((1+sinx)cancel((1-sinx)))/(cancel((1-sinx))cosx)# #=1/cosx +(sinx)/cosx# #=secx +tanx# 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 1389 views around the world You can reuse this answer Creative Commons License