How do you prove tan(x/2)= sinx+cosxcotx-cotx? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Topscooter Dec 21, 2015 Develop the right side. Explanation: We know that tan(x/2) = (1 - cos(x))/sin(x). So we develop the right side of the equality. cot(x) = 1/tan(x) so : sin(x) + cos(x)cot(x) - cot(x) = (sin^2(x) + cos^2(x) - cos(x))/sin(x) = (1-cos(x))/sin(x) = tan(x/2). 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 1646 views around the world You can reuse this answer Creative Commons License