fx=2cos²ωx+2sinωxcosωx+1
＝1+cos2ωx+sin2ωx+1
＝√2sin（2ωx+π/4)+2
T=2π/ω,π/2=2π/2ω,ω=2
f(x)=√2sin（x+π/4)+2
f(x)最大值=2+√2
2Kπ+π/2=x+π/4
x=2Kπ+π/4