Prove that `cos theta + cos[(2pi)/3 + theta] + cos [(4pi)/(3) + theta] = 0`.

Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=0

Prove that cos theta +cos ((2pi)/(3)-theta)+cos ((2pi)/(3)+theta)=0

Prove that : cos^2 theta+ cos^2 ((2pi)/3 -theta) + cos^2 ((2pi)/3 +theta) = 3/2

Prove that cos (pi + theta) = - cos theta

Prove that: 2cos theta cos((pi)/(3)+theta)cos((pi)/(3)-theta)=cos3 theta

If cos^(3) theta + cos^(3)((2pi)/(3) + theta) + cos^(3)((4pi)/(3) + theta) = a cos 3 theta , then a =

Prove that cos theta + cos (120^(@) + theta) + cos ( 120^(@)-theta) =0. Hence deduce that cos ^(3) theta + cos ^(3) ( 120^(@) + theta ) + cos^3( 120^(@)-theta) = 3/4 cos 3 theta.

Prove that: cos^(2)theta+cos^(2)((pi)/(3)+theta)+cos^(2)((pi)/(3)-theta)=(3)/(2)