【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)(1)求函数最小正周期和对称轴方程(2)求函数f(x)在区间[-π/12,π/2]上的值域

问题描述:

【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)
(1)求函数最小正周期和对称轴方程
(2)求函数f(x)在区间[-π/12,π/2]上的值域

f(x)=cos2xcos5π/3+sin2xsin5π/3+2sin(x+π/4-π/2)sin(x+π/4)=1/2cos2x-√3/2sin2x-2cos(x+π/4)sin(x+π/4)=1/2cos2x-√3/2sin2x-sin(2x+π/2)=-1/2cos2x-√3/2sin2x=-sin(2x+π/6)(1)函数最小正周期T=2π/2=π...