向量a=(sinx+cosx,√3sinx),b=(sinx-cosx,2cosx),
f(x)=ab+√3/2
=（sinx+cosx)(sinx-cosx)+2√3sinxcosx+√3/2
= -(cos²x-sin²x)+√3sin2x+√3/2
=√3sin2x-cos2x+√3/2
=2(√3/2*sin2x-1/2*cos2x)+√3/2
=2sin(2x-π/6)+√3/2
sin(2x-π/6)=0时,得到曲线对称中心
∴2x-π/6=kπ,k∈Z
得x=kπ/2+π/12,k∈Z
∴曲线对称中心(kπ/2+π/12,√3/2),k∈Z
2
∵x∈(0,π/2]
∴-π/6