Question

cos a +cos (120-a)+cos (120+a)=0

Answer 1

identity, cos(A + B) + cos(A - B) = 2cos(A)cos(B)

==> cos(120 + A) + cos(120 - A) = 2cos(120)cos(A) = 2(-1/2)cos(A) = - cos(A)

[Since cos(120) = cos(180 - 60) = -cos(60) = 01/2]

Thus, cos(A) + cos(120 + A) + cos(120 - A) = cos(A) - cos(A) = 0 [Proved]

hope this helped you