f（x）
=（1/2)cos²x-√3sinxcosx-（1/2）sin²x+1
=(1/2)cos2x-(√3/2)sin2x+1
=cos(2x+π/3)+1
(1)
最小正周期=2π/2=π
x∈[0,π/2]
2x+π/3∈[π/3,4π/3]
cos(2x+π/3)∈[-1,1/2]
cos(2x+π/3)+1∈[0,3/2]
最大值=3/2,最小值=0
（2）
cos(2x+π/3)+1=9/5
cos(2x+π/3)=4/5
x∈[-π/6,π/6]
2x∈[-π/3,π/3]
2x+π/3∈[0,2π/3]
∴sin(2x+π/3)=3/5
cos2x
=cos(2x+π/3-π/3)
=cos(2x+π/3)cosπ/3+sin(2x+π/3)sinπ/3
=(4+3√3)/10