Question #66d08 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Mar 6, 2017 #LHS=(1-tan^2 x+tan^4 x)# #=((1-tan^2 x+tan^4 x)(1+tan^2x))/(1+tan^2x)# #=((1^2-1xxtan^2 x+(tan^2 x)^2)(1+tan^2x))/(1+tan^2x)# #=(1^3+(tan^2x)^3)/sec^2x# #=cos^2x(1+tan^6x)=RHS# 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 894 views around the world You can reuse this answer Creative Commons License