Question #93493 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Alberto P. Nov 11, 2016 sec^2x/tan^2x+4=5+cot^2x Explanation: sec^2x/tan^2x+4=1/cos^2x*cot^2x+4=1/cancel(cos^2x)*cancel(cos^2x)/sin^2x+4= =(sin^2x+cos^2x)/sin^2x+4=5+cot^2x 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 1620 views around the world You can reuse this answer Creative Commons License