cos^2(x+∏/3)+cos^2(x-∏/3)
=(cosx/2-根号3*sinx/2)^2+(cosx/2+根号3*sinx/2)^2
=(cosx)^2/2+3(sinx)^2/2
=1/2+(sinx)^2
f(x)=cos^2x+cos^2(x+∏/3)+cos^2(x-∏/3)
=(cosx)^2+1/2+(sinx)^2
=3/2,
是常数,得证.