How do you prove 1-cosx^2/(1+sinx)= sinx? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Anees Apr 15, 2015 Solution 1-(cos^2x)/(1+sinx)=sinx....(i) As cos^2x=1-sin^2x So, L.H.S of equation no. (i) =1-(1-sin^2x)/(1+sinx) =1-((1-sinx)(1+sinx))/((1+sinx)) =1-((1-sinx)cancel((1+sinx)))/cancel((1+sinx)) =1-(1-sinx) =1-1+sinx =cancel1-cancel1+sinx =sinx =R.H.S 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 5200 views around the world You can reuse this answer Creative Commons License