已知函数F(X)=2sin x cos x -2sin 2x (x €r )

题目

已知函数F(X)=2sin x cos x -2sin 2x (x €r )
①求最小正周期②求函数在【π/24.π/4】上的值域

答案

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]