Question

prove cos x + cos(120-x) + cos(120+x) = 0

Answer 1

hiiii friend,

cosx + cos (120-x) + cos (120+x)
=>. cosx + 2cos [(120-x+120+x) /2] cos [(120-x-120-x) /2]
=>. cosx + 2cos120 cos(-x)
=>. cosx + 2cos(180-60) cosx
=>. cosx + 2 (-cos 60) cosx
=>. cosx - 2 × 1/2 cosx
=>. cosx - cosx
=>. 0 hence proved....

Answer 2

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

L.H.S

cos x+ 2 cos (120-x +120 + x)/2.cos (120- x
-120-x)
[ cos C + cos D = 2 cos (C+D)/2.cos(C-D)/2]

= cos x + 2 cos 120 .cos(-x). [cos120= -1/2]
[cos (-x) = cos x ]
= cos x + 2×-1/2.cosx
= cos x - cos x
= 0
R.H.S
Proved