Question

prove cos x + cos 2x + cos 3x =0

Answer 1

cos x + cos 2x + cos 3x = 0

=> cos 3x + cos x + cos 2x = 0

=> cos [(3x-x)/2] 2cos [(3x+3)/2] + cos 2x

=> 2cos 2x.cos x + cos 2x = 0

=> cos 2x [2cosx+1] = 0

=> cos 2x = 0

=> 2x = (2n+1) pi /2

n belongs to z