Question #49d56 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer salamat ยท seol Mar 30, 2017 see explanation Explanation: let's take the left hand side (abbr. LHS) to prove the right hand side (abbr. RHS)... (csc x - sin x)/cos x = \color(indianred)((1/sin x) -sin x)/cos x = \color(indianred)((1 - sin^2 x)/sin x)\times1/cos x = (1 - sin^2 x)/(sin x cos x) = cos^cancel(2)x/(sin x cancelcos x) = cos x/sin x = cot x \color(green)(\sqrt()) 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 1451 views around the world You can reuse this answer Creative Commons License