y=2√3 sinxcosx+2cos²x
=√3 sin2x+cos2x+1
=2(√3/2sin2x+1/2*cos2x)+1
=2(sin2xcosπ/6+cos2xsinπ/6)+1
=2sin(2x+π/6)+1
T=2π/2=π
当2x+π/6=π/2时,函数y值最大,最大值为：3