f(x)=cos2x(√3sin2x-cos2x)
=√3sin2xcos2x-cos²2x
=(√3/2)sin4x-(1+cos4x)/2
=(√3/2)sin4x-(1/2)cos4x-1/2
=sin(4x+π/6)-1/2
T=2π/4=π/2