f(x)=cos(2x－π/3)+2sin(x－π/4)sin(x+π/4)的对称轴方程,在〖—π/12.π/2〗的值域

题目

f(x)=cos(2x－π/3)+2sin(x－π/4)sin(x+π/4)的对称轴方程,在〖—π/12.π/2〗的值域

答案

f（x）=1/2 cos2x+√3/2 sin2x-cos2x=√3/2 sin2x-1/2cos2x
=sin（2x-π/6）
2x-π/6∈[-π/3,5π/6]
f（x）∈[-√3/2,1]