How do you prove tan(2theta)=2/(cottheta-tantheta)? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Oct 7, 2016 see below Explanation: tan 2 theta = 2/(cot theta-tan theta) Right Side :=2/(cot theta-tan theta) =2/(costheta/sin theta - sin theta/cos theta) =2/((cos^2theta-sin^2theta)/(sin theta cos theta) =2 * (sin theta cos theta)/(cos^2theta-sin^2theta) =(2 sin theta cos theta)/(cos^2theta-sin^2theta) =sin(2theta)/cos(2theta) =tan ( 2 theta) :. = Left Side 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 4854 views around the world You can reuse this answer Creative Commons License