How do you verify the identity #cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Nghi N. Apr 29, 2015 Use the trig identity: #cos 2a = 1 - 2.sin^2 a# #cos 4x = 1 - 2.sin^2 (2x)# #cos 2x = 1 - 2sin^2 (x)# #y = cos 4x + cos 2x = 2 - 2.sin^2 (2x) - 2.sin^2 (x)#. 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 21240 views around the world You can reuse this answer Creative Commons License