`cos alpha+ cos(120^@ +alpha)+ cos(120^@ -alpha)=0`

Prove that cos alpha cos (120^(@) + alpha) cos (240^(@) + alpha) = 1/4 cos 3 alpha

Prove that cos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha.

Show that, cos^(2)alpha + cos^(2) (120^(@) - alpha) + cos^(2) (120^(@) + alpha) = 3/2.

cos^(3)alpha+cos^(3)(120+alpha)+cos(120-alpha)=3(sqrt(3))/(4), then the general solution of alpha is

Assertion (A):cos^(2)theta+cos^(2)(60^(@)-theta)+cos^(2)(60^(@)+theta)=(3)/(2)sin alpha-sin(120^(@)-alpha)+sin(120^(@)+alpha)=0

Assertion (A):cos^(2)theta+cos^(2)(60^(@)-theta)+cos^(2)(60^(@)+theta)=(3)/(2)sin alpha-sin(120^(@)-alpha)+sin(120^(@)+alpha)=0

Prove that, cos^(3) alpha + cos^(3) (120^(@) + alpha) + cos^(3) (240^(@) + alpha) = 3/4 cos 3 alpha

(cos alpha + 2 cos 3 alpha + cos 5 alpha )/(cos 3 alpha + 2 cos 5 alpha + cos 7 alpha ) = cos 3 alpha sec 5 alpha .