How do you prove #csc^2xtan^2x-1=tan^2x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Nghi N. Jul 3, 2015 Prove trig identity Explanation: #(1/(sin^2 x))(sin^2 x/cos^2 x) - 1 = # #= (sin^2 x - sin^2 x.cos^2 x)/(sin^2 x.cos^2 x)# = #((sin^2 x)(1 - cos^2 x))/(sin^2x.cos^2 x) = # =#sin^2x/cos^2 x = tan^2 x# 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 32437 views around the world You can reuse this answer Creative Commons License