How do you verify (1 + csc x)(sec x - tan x) = cot x? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Jarni Renz Mar 5, 2016 RHS=cotx Explanation: RHS: (1 + cscx)(secx-tanx) (1 + 1/sinx)(1/cosx-sinx/cosx) ((sinx + 1)/sinx)((1-sinx)/cosx) (cancelsinx-sin^2x+1-cancelsinx)/(sinxcosx) (1-sin^2x)/(sinxcosx) (cancel(cos^2x)^cosx)/(sinxcancelcosx) cosx/sinx cotx=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 12098 views around the world You can reuse this answer Creative Commons License