How do you prove #tan^2xsin^2x=tan^2x + cos^2x-1#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Nghi N. May 21, 2015 #tan^2 x .sin^2 x = tan^2 x(1 - cos^2 x) = tan^2 x - tan^2 x(cos^2 x)# #= tan^2 x - (sin^2 x.cos^2 x)/(cos^2 x) = tan^2 x - sin^2 x =# #= tan^2x - 1 + cos^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 4851 views around the world You can reuse this answer Creative Commons License