y=[ sin^2(x)+cos^2(x) ] + sin(2x) + 2cos^2(x)=1+sin2x +(1+cos2x)=
=sin2x+cos2x+2=根号(2)*sin(2x+π/4)+2
当2x+π/4=π/2+2kπ时,即x=π/8+kπ时,y 取最大值,y(MAx)=2 + 根号(2)
当2x+π/4= - π/2+2kπ时,即x=-3π/8+kπ时,y 取最小值,y(min)=2- 根号(2)
(2) -π/2+2kπ≤2x+π/4≤π/2+2kπ 得 -3π/8+kπ≤x≤π/8+kπ