How do you prove (cosx/(1 + sinx)) + (cosx/(1 - sinx)) = 2secx? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Mar 6, 2018 See Below Explanation: LHS: cosx /(1+sinx) + cos x/(1-sinx) =(cosx(1-sinx)+cosx(1+sinx))/(1-sin^2x)-->common denominator =(cosx-sin x cos x+cosx+sinx cos x)/cos^2x =(cosxcancel(-sin x cos x)+cosx+cancel(sinx cos x))/cos^2x =(2cosx)/cos^2x =(2cancelcosx)/cos^cancel2x =2/cosx =2*1/cosx =sec x =RHS 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 29150 views around the world You can reuse this answer Creative Commons License