y=2sinx(sinx+cosx)=2(sinx)^2+2sinxcosx=1-2(sinx)^2+sin2x-1=cos2x+sin2x-1=根2sin(45度+2x)-1.由题可知,2x+45度属于[-45度,45度],所以x属于[-90度,0度],ymax=根2-1,ymin=-根2-1.第二问：y=(sinx+cosx)^2+2(cosx)^2=1+2cosxsinx+2(cosx)^2-1+1=2+sin2x+cos2x=2+根2sin(45度+2x)