f(x)=向量a.向量b
=sinxcos(x+π/3)+√3/4.
=(1/2)[sin(x+x+π/3)+sin(x-(x+π/3)]+√3/4.
=(1/2)[sin(2x+π/3)-sinπ/3]+√3/4
=(1/2)[sin(2x+π/3)-√3/2]+√3/4
=(1/2)sin(2x+π/3)-√3/4+√3/4.
∴f(x)=(1/2)sin(2x+π/3).
(1) 当sin(2x+π/3)=1,即 2x+π/3=π/2.x=π/12时,f(x)具有最大值,f(x)max=(1/2).
当sin(2x+π/3)=-1,即 2x+π/3=3π/2,x=7π/12时,f(x)具有最小值,f(x)min=-(1/2).
∵sinx的单调递减区间为：2kπ+π/2