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