已知向量m=(cosx,-sinx),向量n=(cosx,sinx-2根号3cosx),x∈R,设f（x）=向量n*向量m.（）

解 ：f(x)=向量m.向量n.
=cos^2x,+(-sinx)*(sinx-2√3cosx).
=cos^2x-sin^2x+2√3sinxcosx.
=cos2x+√3sin2x.
=2(1/2)cos2x+(√3/2)sin2x.
=2sin(2x+π/6).
(1）T=2π/2=π.---答1.
(2).f(x)=2sin(2x+π./6).π/4≤x≤π/2.,2π/3≤2x+π/6≤π+π/6.
f(x)=2sin(2π/3)=2sin(π-π/3=2sin(π/3)=2*√3/2=√3.
f(x)=2sin(π+π/6)=-2sin(π/6)=-2*(1/2)=-1.
∴f(x)的值域为：[-1,√3].