How do you prove #2sin^2thetacos^2theta+cos^4theta=1-sin^4theta#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Oct 6, 2016 see below Explanation: #2sin^2 theta cos^2 theta + cos ^4 theta=1-sin^4 theta# Left Side :#=2sin^2 theta cos^2 theta + cos ^4 theta# #=cos^2 theta (2sin^2 theta+cos^2 theta)# #=cos^2 theta (2sin^2 theta+1-sin^2 theta)# #=cos^2 theta (2sin^2 theta-sin^2 theta+1)# #=cos^2 theta (sin^2theta +1)# #=(1-sin^2 theta)(1+sin^2 theta)# #=1-sin^4 theta# #=# Right Side 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 4167 views around the world You can reuse this answer Creative Commons License