साबित करें कि
`cos^(2) theta + cos^(2)((2pi)/(3)-theta)+cos^(2)((2pi)/(3) + theta) = (3)/(2)`

Explanation

बायाँ पक्ष `= (1)/(2) (1+cos2 theta) + (1)/(2) [ 1+ cos ((4pi)/(3) + 2theta)]+(1)/(2) [ 1+ cos ((4pi)/(3)+2theta)]`
`= (3)/(2)+(1)/(2)[ cos 2 theta + cos ((4pi)/(3) - 2theta) + cos ((4pi)/(3) + 2theta)]`
`= (3)/(2) + (1)/(2) cos 2 theta + (1)/(2). 2cos . ( 4pi)/(3) cos 2 theta [ cos C + cos D ` के सूत्र से]
`= (3)/(2) + (1)/(2) cos 2theta + cos .(4pi)/(3) cos 2 theta`
`= (3)/(2)+ (1)/(2) cos 2 theta - cos ( pi - ( pi)/(3))cos 2 theta `
`= (3)/(2) + (1)/(2) cos 2 theta - cos. ( pi)/(3) cos2 theta ` `[ :' cos ( pi + theta ) = - cos theta ]`
` = (3)/(2) + (1)/(2) cos 2 theta - (1)/(2) cos 2 theta = (3)/(2)` `[ :' cos . ( pi )/(3) = (1)/(2) ]`