(1)a⊥b则：f(x)=sinxcosx+√3cosxcosx=sin2x/2+√3(1+cos2x)/2=sin(2x+π/3)+√3/2=0∴2x+π/3=2kπ+3π/2±π/6∴x=kπ+7π/12±π/12(2)f(x)=sin(2x+π/3)+√3/2∴f(x)周期为π，递增区间为[kπ-5π/12,kπ+π/12]
