Prove #Cos^2A+Sin^2A*cos2B=cos^2B+sin^2B*cos2A#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Abhishek K. Mar 9, 2018 #LHS=cos^2A+sin^2A*cos2B# #=1/2[2cos^2A+2sin^2A*cos2B]# #=1/2[1+cos2A+(1-cos2A)*cos2B# #=1/2[1+cos2A+cos2B-cos2A*cos2B# #=1/2[{1+cos2B}+{cos2A(1-cos2B)}]# #=1/2[2cos^2B+2sin^2B*cos2A]# #=cos^2B+sin^2B*cos2A=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 24777 views around the world You can reuse this answer Creative Commons License