Question #eabbb Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Mar 2, 2017 see below Explanation: Use the formulas #cos x+cos y =2 cos (1/2 (x+y))cos(1/2(x-y))# and #cos(-x)=cosx# Right Hand Side: #1/2 [cosx+cos 3x]=1/2 [2cos (1/2 (x+3x))cos(1/2(x-3x))]# #=1/cancel2 cancel2cos (1/2 (x+3x))cos(1/2(x-3x))# #=cos (1/2 (4x))cos(1/2(-2x))# #=cos 2x*cos(-x)# #=cos2x cos x# #=cosx cos 2x# #:.=#Left Hand 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 1230 views around the world You can reuse this answer Creative Commons License