f(x)=sinx×sin(x+π/2)-√3cos²（3π+x）+√3/2
=sinx*cosx-√3/2(2cos^2x-1)
=1/2sin2x-√3/2cos2x
=sin(2x-π/3)
f(x)的最小正周期=2π/2=π
增区间
2kπ-π/2