f(x)=√2/2cos(2x+π/4)+sin²x=√2/2(√2/2cos2x-√2/2sin2x)+(1-cos2x)/2
=1/2cos2x-1/2sin2x+1/2-1/2cos2x
=﹣1/2sin2x+1/2
∴最小正期T=2π/2=π
f(x)=√2/2cos(2x+π/4)+sin²x=√2/2(√2/2cos2x-√2/2sin2x)+(1-cos2x)/2
=1/2cos2x-1/2sin2x+1/2-1/2cos2x
=﹣1/2sin2x+1/2
∴最小正期T=2π/2=π