答：
f(x)=(sinx)^2-2sinxcosx+3(cosx)^2
=(sinx)^2+(cosx)^2-sin2x+2(cosx)^2
=1-sin2x+cos2x+1
=cos2x-sin2x+2
=√2*[(√2/2)cos2x-(√2/2)sin2x]+2
=√2*cos(2x+π/4)+2
最小正周期T=2π/2=π