Question #fa425 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Sidharth Mar 14, 2016 Please look below Explanation: Lets start with RHS; #(1 + cosx)/ 2 = (1 + cos(2 * x/2))/ 2 = (1 + cos^2 (x/2) - sin^2 (x/2))/2 # # = ( cos^2 (x/2) +sin^2 (x/2) + cos^2 (x/2) - sin^2 (x/2))/2# # = ( cos^2 (x/2) +cancel(sin^2 (x/2)) + cos^2 (x/2) cancel(- sin^2 (x/2)))/2# # =( cancel(2)cos^2(x/2))/cancel2 = cos^2 (x/2) = LHS# Hence Verified 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 3737 views around the world You can reuse this answer Creative Commons License