How do you prove #Cosx + sinx tanx = secx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Typo Jun 24, 2018 Proof in explanation. Explanation: Proving #cosx + sinxtanx -= secx# #RHS = cosx + sinxtanx# #=cosx + sinx*sinx/cosx# #=cosx+sin^2x/cosx# #=cos^2x/cosx +sin^2x/cosx# #=(sin^2x+cos^2x)/cosx# [Pythagorean identity: #sin^2x+cos^2x=1#] #=1/cosx# #=secx = LHS# 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 10558 views around the world You can reuse this answer Creative Commons License