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 1476 views around the world You can reuse this answer Creative Commons License