Question #562b9 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Dec 3, 2016 To prove 1+tanxtan2x=tan2xcotx-1 LHS=1+tanxtan2x =1+(tanx xx2tanx)/(1-tan^2x) =(1-tan^2+2tan^2x)/(1-tan^2x) =(1+tan^2x)/(1-tan^2x) =(2-1+tan^2x)/(1-tan^2x) =(2-(1-tan^2x))/(1-tan^2x) =2/(1-tan^2x)-(1-tan^2x)/(1-tan^2x) =(2tanxcotx)/(1-tan^2x)-1 =tan2xcotx-1=RHS Proved 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 1144 views around the world You can reuse this answer Creative Commons License