Question #200ab Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub May 2, 2016 see below Explanation: Left Side#= cos^4x (1+sin^4x/cos^4x)# #=cos^4x xx (cos^4x+sin^4x)/cos^4x# #=cos^4x+sin^4x# #= cos^2x cos^2x+ sin^2x sin^2x# #=(1-sin^2x)cos^2x+(1-cos^2x)sin^2x# #=cos^2x-sin^2xcos^2x+sin^2x-sin^2xcos^2x# #=cos^2x+sin^2x-2sin^2xcos^2x# #=1-2sin^2xcos^2x# #=#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 1061 views around the world You can reuse this answer Creative Commons License