`cos^2 A + cos^2 (A+(2pi)/3) + cos^2 ( A-(2pi)/3) = 3/2`

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

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

Prove that: cos^(3)A + cos^(3)((2pi)/(3)+A) + cos^(3)((4pi)/3+A) = 3/4 cos3A

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

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

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

cos^(2)((3 pi)/(5))+cos^(2)((4 pi)/(5))=

cos ^ (2) ((pi) / (3)) + cos ^ (2) ((2 pi) / (3)) + cos ^ (2) ((4 pi) / (3)) + cos ^ ( 2) ((8 pi) / (3)) =

cos ^ (2) (0) + cos ^ (2) ((pi) / (6)) + cos ^ (2) ((pi) / (3)) + cos ^ (2) ((pi) / ( 2))