f(x)=sin(2x-π/4)-2√2sin²x＝sin2xcosπ/4-cos2xsinπ/4-√2(1-cos2x)=√2/2 sin2x- √2/2 cos2x +√2cos2x-√2=√2/2 sin2x+√2/2 cos2x-√2=sin(2x+π/4)-√2∴最小正周期是2π/2=π