题目应该是：F(x)=2sinxcosx-2sinx^2
=sin2x-(1-cos2x)
=sin2x+cos2x-1
=√2sin(2x+π/4)-1
∴f(x)最小正周期=2π/2=π
x∈[π/24,π/4]
2x+π/4∈[π/3,3π/4]
∴f(x)∈[0,√2-1]