How do you verify (1-cos2t)/ sin t= 2 sin t? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer GiĆ³ May 13, 2015 use the fact that cos2t=cos^2t-sin^2t to get (1-cos^2t+sin^2t)/sint=2sint But 1=sin^2t+cos^2t So: (sin^2t+cancel(cos^2t)-cancel(cos^2t)+sin^2t)/sint=2sint (2sin^cancel(2)t)/cancel(sint)=2sint 2sint=2sint 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 2645 views around the world You can reuse this answer Creative Commons License