How do you verify the identity #(2tanx)/(1+tan^2x) =sin2x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer GiĆ³ Apr 30, 2015 Use the fact that: #tanx=sinx/cosx# and #sin2x=2sinxcosx# So: #2sinx/cosx*1/(1+sin^x/cos^2x)=2sinxcosx# #2sinx/cosx*cos^2x/(cos^2x+sin^2x)=2sinxcosx# #2sinx/cancel(cosx)*cos^cancel(2)x/(cos^2x+sin^2x)=2sinxcosx# But #sin^2x+cos^2x=1# So: #2sinxcosx=2sinxcosx# 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 42829 views around the world You can reuse this answer Creative Commons License