解，f(x)=√2sinⅹcosπ/4+√2cosxsinπ/4 =√2sin(x+π/4)f(x)为非奇非偶，f(x)在[-3π/4+2kπ，π/4+2kπ]↑ f(x)在(π/4+2kπ，5π/4+2kπ)↓其中k为整数。f(x)最大为f(π/2)=1
