y=sin^2x+sinxcosx+2cos^2x=sin^2x+1/2*sin2x+2cos^2x=1+1/2*sin2x+cos^2x=1+1/2*sin2x+(cos2x+1)/2=3/2+1/2*(sin2x+cos2x)=3/2+√2/2*sin2x从而值域是[3/2-√2/2,3/2+√2/2]可以吗?