How do you prove # 1/(secx-tanx) - 1/(secx+tanx)=2tanx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub May 11, 2016 see below Explanation: Use Property: #sec^2x=1+tan^2x# Left Side:#=1/(secx-tanx) -1/(secx+tanx)# #=(secx+tanx-(secx-tanx))/((secx-tanx)(secx+tanx))# #=(secx+tanx-secx+tanx)/(sec^2x-tan^2x)# #=(2tanx)/1# #=2tanx# #=# 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 10783 views around the world You can reuse this answer Creative Commons License