y=sin²x+cos²x+2sinxcosx+2(1+cos2x)/2
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
所以最大值=√2+2
最小值=√2/2
递减则2kπ+π/2<2x+π/4<2kπ+3π/2
kπ+π/8所以减区间(kπ+π/8,kπ+5π/8)