f(x)=(sin²x+cos²x)+2sinxcosx+2cos²x=1+sin2x+2cos²x=sin2x+(2cos²x-1)+2=sin2x+cos2x+2=2sin(2x+π/4)+2当2x+π/4=2kπ+π/2即x=kπ+π/8f(x)max=2+√2当2x+π/4=2kπ-π/2即x=kπ-3π/8...