Prove that :
`cos^(2)A+cos^(2)(A+pi/3)+cos^(2)(A-pi/3)`
`=1/2[2cos^(2)A+2cos^(2)(A+60^(@))+2cos^(2)(A-60^(@))]`
`=1/2[1+cos2A+1+cos(2A+120^(@))+1+cos(2A-120^(@))]`
`1/2[3+cos2A+cos(2A+120^(@))+cos(2A-120^(@))]`
`1/2[3+cos2A+2cos(2A+120^(@)+2A-120^(@))/(2).cos(2A+120^(@)-2A+120^(@))/(2)]`
`=1/2[3+cos2A+2cos2Acos120^(@)]`
`=1/2[3cos2A+2cos2Acos(90^(@)+30^(@))]`
`=1/2[3+cos2A-2.cos2A.(1/2)]`
`=1/2(3+cos2A-cos2A)`
`=3/2`= RHS Hence Proved.