作业帮已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求函数f(x已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)求函数f(x)的最小正周期和图像的对称轴方程,求函数f(x)在区间[-π/12,π/2]上的值域
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已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求函数f(x已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)求函数f(x)的最小正周期和图像的对称轴方程,求函数f(x)在区间[-π/12,π/2]上的值域
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求函数f(x
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
求函数f(x)的最小正周期和图像的对称轴方程,求函数f(x)在区间[-π/12,π/2]上的值域
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4) 求函数f(x已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)求函数f(x)的最小正周期和图像的对称轴方程,求函数f(x)在区间[-π/12,π/2]上的值域
sin(x+π/4)=sin(x-π/4+π/2)=cos(x-π/4)
所以原式=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)=cos(2x-π/3)+sin(2x-π/2)=1/2cos(2x)+√3/2sin(2x)-cos(2x)=√3/2sin(2x)-1/2cos(2x)=-cos(2x+60)
最小正周期=2π/2=π 对称轴=kπ/2 根据图像和单调性可知,当x=-π/12时,函数得最小值-√3/2,当x=π/2时,函数得最大值√3/2,所以函数在区间上的值域为【-√3/2,√3/2】