f（x）=2cos²x+√3sin2x+a
=2cos²x-1+√3sin2x+a+1
=cos2x+√3sin2x+a+1
=2（1/2 cos2x+√3/2sin2x）+a+1
=2sin（2x+π/6）+a+1
∵-π/6≤x≤π/6
∴-π/3≤2x≤π/3
∴-π/6≤2x+π/6≤π/2
∴f（x）max=2+a+1=3
解得：a=0