f（x）=√2/2sin（2X+π/4）+sin^2x
=√2/2*sin2x*√2/2+√2/2*cos2x*√2/2+sin^2x
=1/2sin2x+1/2cos2x+sin^2x
=1/2sin2x+cos^2x-1/2+sin^2x
=1/2sin2x+1-1/2
=1/2sin2x + 1/2
f（x）的最小正周期=2π/2=π
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