How do you prove (csc+cot)(csc-cot)=1? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Rafael Oct 17, 2015 csc^2theta=1+cot^2theta is a trigonometric identity. Explanation: [1]color(white)(XX)(csctheta+cottheta)(csctheta-cottheta)=1 Property: (a+b)(a-b)=a^2-b^2 [2]color(white)(XX)csc^2theta-cot^2theta=1 [3]color(white)(XX)csc^2theta=1+cot^2theta This is a trigonometric identity. 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 4426 views around the world You can reuse this answer Creative Commons License