f(x)=√2/2cos(2x+π/4)+sin²x
=1/2cos2x-1/2sin2x+1/2-1/2cos2x
=1/2-1/2sin2x
∵sin2x∈[-1,1]
∴f(x)∈[0,1]
∴f(x)的最大值为1,最小值为0