सिद्ध कीजिए कि - `cos^(2)x + cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)`.

Explanation

`L.H.S. = 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)[3+cos 2x+cos (2x +(2pi)/(3))+cos(2x-(2pi)/(3))]`
`= (1)/(2)[3+cos 2x+2cos 2x."cos"(2pi)/(3)]`
`rArr " " L.H.S. =(1)/(2)[3+cos 2x+2 cos 2x cos(pi-(pi)/(3))]`
`=(1)/(2)[3+cos 2x-2cos x cos.(pi)/(3)]`
`=(1)/(2)[3+cos 2x-cos 2x]=(3)/(2)=R.H.S. " "` इति सिद्धम्