因f(x)=m·n
=(1,sinx)·(1/2cos2x-√3/2sinx,2sinx)
=1/2cos2x-√3/2sinx+2sin^2x
=1/2(1-2sin^2x)-√3/2sinx+2sin^2x
=sin^2x-√3/2sinx+1/2
=(sinx-√3/4)^2+5/16
则f(x)为周期函数,最小正周期T0=2π
因0≤x≤π/2
则0≤sinx≤1
即有-√3/4≤sinx-√3/4≤1-√3/4
即有0≤(sinx-√3/4)^2≤(1-√3/4)^2
所以5/16≤f(x)≤(1-√3/4)^2+5/16
即5/16≤f(x)≤(3-√3)/2