y=4cos^2x-2+4√3sinxcosx
=2(2cos^2x-1) +4√3sinxcosx
=2cos2x+2√3sin2x
=4[(√3/2)sin2x+1/2cos2x]
=4sin(2x+π/6)
函数的最小正周期是2π/2=π.
函数的最大值是4,此时2x+π/6=2kπ+π/2,k∈Z.
则x= kπ+π/6,k∈Z.