Question #df912 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Dec 18, 2016 #cos^6 A + sin^6A# #=(cos^2A)^3 + (sin^2A)^3# #=(cos^2A +sin^2A)^3-3cos^2Asin^2A(cos^2+sin^2A)# #=1^3-3/4*4cos^2A*sin^2A*1# #=1-3/4*(2cosA*sinA)^2# #=1-3/4*(sin2A)^2# #=1-3/4*sin^2 2A=RHS# Proved 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 1612 views around the world You can reuse this answer Creative Commons License