f(x)=向量a.向量b.
=2cosx*cos(x-π/3)+sinx*√3sinxcosx-sin^2x.
=2cosx[cosxcos(π/3)+sinxsin(π/3)]+(√3/2)*2sinxcosx-sin^2x.
=2cos^2x*(1/2)+2sinxcosx(√3/2)+(√3/2)sin2x-sin^2x..
=cos^2x-sin^2x+(√3/2)sin2x+(√3/2)sin2x.
=cos2x+√3sin2x.
=2[cos2x*(1/2)+(√3/2)sin2x.
=2sin(2x+π/6).
∵sinx的单调递减区间为:x∈(2kπ+π/2,2kπ+3π/2).
由 2kπ+π/2