SOLUTION: Proove that CosA+cos(120+A)+cos(120-A)=0

Use the addition formula for cosine

    cos(alpha + beta) = cos(alpha)*cos(beta) - sin(alpha)*sin(beta)

(see the lesson Addition and subtraction formulas in this site). You will have 


cos(120+A) = cos(120)*cos(A) - sin(120)*sin(A),

cos(120-A) = cos(120)*cos(A) + sin(120)*sin(A).


Add these two equality (both sides). You will get

cos(120+A) + cos(120-A) = 2cos(120)*cos(A).

Now use that cos(120) = .  Hence 2cos(120) = -1.

Hence,

cos(A) + cos(120+A) + cos(120-A) = cos(A) + 2cos(120)*cos(A) = cos(A) - cos(A) = 0.

QED.