How do you prove #sin(2theta)/sintheta-cos(2theta)/costheta=sectheta#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Oct 5, 2016 see below Explanation: #sin(2theta)/sin theta - cos(2theta)/cos theta = sec theta# Left Side: #=sin(2theta)/sin theta - cos(2theta)/cos theta# #=(2sin theta cos theta)/sin theta - (2cos^2theta-1)/cos theta# #=2cos theta-(2cos^2theta/cos theta-1/cos theta)# #=2cos theta-2cos theta+1/cos theta# #=1/cos theta# #=sec theta# #=# Right 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 9928 views around the world You can reuse this answer Creative Commons License