How do you verify the identity #cosx(tan^2x+1)=secx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Monzur R. Feb 26, 2017 We have to use the common identity: #sin^2x+cos^2x=1#. Dividing each term by #cos^2x#, we get #tan^2x+1=sec^2x#. So #cosx(tan^2x+1)=cos(sec^2x)=cancel(cosx)1/cancel(cos^2x)=1/cosx=secx# 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 19677 views around the world You can reuse this answer Creative Commons License