How do you verify #sec^2((pi/2)-x)-1=cot^2 x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer ProfLayton Apr 22, 2016 Proof below Explanation: Identity: #sec^2theta=1+tan^2theta# #sec^2(pi/2-x)-1=1+tan^2(pi/2-x)-1# #=tan^2(pi/2-x)# Identity: #tan(pi/2-theta)=cottheta# #=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 5338 views around the world You can reuse this answer Creative Commons License