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

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

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

the value of cos^(2)theta+cos^(2)((2 pi)/(3)-theta)+cos^(2)((2 pi)/(3)+theta) is (a) 3 (b) (1)/(2)(c)(3)/(2) (d)none of these

If theta lies in the first quadrant and cos theta=(8)/(17), then prove that cos((pi)/(6)+theta)+cos((pi)/(4)-theta)+cos((2 pi)/(3)-theta)=((sqrt(3)-1)/(2)+(1)/(sqrt(2)))(23)/(17)

Prove that: cos^(2)((pi)/(4)-theta)-sin^(2)((pi)/(4)-theta)=s in2 theta

Prove that: cos^3theta+cos^3 (theta- (2pi)/n)+cos^3 (theta- (4pi)/n)+… to n terms =0

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

Prove that: (sin theta - 2 sin^(3) theta) = (2cos^(3) theta - cos theta) tan theta .