#If tan^4a + tan^2a = 1#, then find the value of #cos^4a + cos^2a ?# Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Dec 26, 2016 Given #tan^4a+tan^2a=1# #=>(tan^2a+1)tan^2a=1# #=>sec^2atan^2a=1# #=>(1/cos^2a)tan^2a=1# #=>tan^2a=cos^2a# #=>sin^2a/cos^2a=cos^2a# #=>sin^2a=cos^4a# #=>1-cos^2a=cos^4a# #=>cos^4a+cos^2a=1# 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 37676 views around the world You can reuse this answer Creative Commons License