f(x)=向量a×向量b=(sinx,√3cosx)*(cosx,cosx)
=sinxcosx+√3cosxcosx
=1/2(2sinxcosx+2√3cosxcosx)
=1/2(sin2x+√3cos2x+√3)
=1/2sin2x+√3/2cos2x+√3/2
=cosπ/3sin2x+sinπ/3cos2x+√3/2
=sin(2x+π/3)+√3/2
(1)sin(2x+π/3)+√3/2 =0
sin(2x+π/3)=-√3/2
2x+π/3=2kπ-π/3
x=kπ-π/3
(2)T=2π/2=π
由2kπ-π/2≤2x+π/3≤2kπ+π/2
解得增区间为：kπ-5π/12≤x≤kπ+π/12