The value of the expression `cos^3theta+cos^3(120+theta)+cos^3(240+theta)` is;

Explanation

`cos 3 theta = 4 cos theta - 3 cos theta`

`cos^3 theta = ( cos 3 theta + 3 cos theta)/4`

`(cos(3 theta) + 3 cos theta + cos ( 360 + 3 theta) + 3 cos( theta + 120) + cos(120+ 3 theta) + 3cos( theta + 240))/4`

`= (cos 3 theta + 3 cos theta + cos 3 theta + 3 cos ( theta+ 120) + cos 30 + 3cos( theta-120))/4`

`= (3 cos 3 theta + 3 cos theta + 3 xx 2 cos theta cos 120)/4`

`= ( 3 cos 3 theta + 3 cos theta + 6 xx (-1/2) cos theta)/4`

`= 3/4 cos 3 theta`

option C is correct

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