Find the value of (secx-1)(secx+1) and 1-sin^2theta/tan^2theta? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Shwetank Mauria Jul 4, 2016 (secx-1)(secx+1)=tan^2x and 1-sin^2theta/tan^2theta=sin^2theta Explanation: (secx-1)(secx+1)=sec^2x-1=1+tan^2x-1=tan^2x 1-sin^2theta/tan^2theta=1-sin^2theta/(sin^2theta/cos^2theta) = 1-sin^2thetaxxcos^2theta/sin^2theta = 1-cos^2theta = sin^2theta 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 1700 views around the world You can reuse this answer Creative Commons License