सिध्द कीजिए।
`cos^(2) +cos^(2) (x+ .(pi)/(3)) +cos^(2) (x-.(pi)/(3)) = (3)/(2)`

Explanation

बायाँ पक्षः `cos^(2) x+ cos^(2) (x+ (pi)/(3)) + cos^(2) (x-.(pi)/(3))`
`=(1+cos 2x)/(2) + (1 + cos (2x +.(2pi)/(3)))/(2) +(1+cos (2x -(2pi)/(3)))/(2)`
`=(1)/(2)[1+ cos 2x +1 + cos (2x + .(2pi)/(3)) +1+ cos (2x -(2pi)/(3))]`
`=(1)/(2)[3+cos 2x +cos (2x + .(2pi)/(3))+ cos (2x -(2pi)/(3))]`
`=(1)/(2)[3 +cos 2x + 2cos ((2x +(2pi)/(3) +2x -(2pi)/(3))/(2)) cos ((2x+ (2pi)/(3) -2x+(2pi)/(3))/(2))]`
`=(1)/(2)[3 +cos 2x + 2 cos 2x cos .(2pi)/(3)]`
`=(1)/(2) [3+ cos 2x+ 2cos 2x cos (pi-(pi)/(3))]`
`=(1)/(2)[3 +cos 2x- 2cos 2x cos .(pi)/(3)]`
`=(1)/(2)[3+cos 2x -cos 2x]`
`=(3)/(2)`
= दायाँ पक्ष।