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

cos^(2)(""(pi)/(6) + theta ) -sin^(2)""((pi)/(6) - theta ) =

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

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

cos((3pi)/2+theta)=

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

Prove that (cos (pi-theta).cot(pi/2 +theta).cos(-theta))/(tan(pi+theta).tan((3pi)/(2)+theta).sin(2pi-theta))=cos theta

Cos^(2)(pi/4-theta/2)-sin^(2)(pi/4-theta/2)=

Prove that (sin(3pi-theta)cos(theta- pi/2)tan((3pi)/(2)-theta))/(cosec((13pi)/(2)+theta)sec(3pi+theta)cot(theta- pi/2))=cos^(4)theta