已知f(x)=2sin(x-π/3)cos(x-π/3)+2根号3cos^2(x-π/3)-根号3 ①求f(x)的最值及取的最值时相应的x的值

题目

已知f(x)=2sin(x-π/3)cos(x-π/3)+2根号3cos^2(x-π/3)-根号3 ①求f(x)的最值及取的最值时相应的x的值
②写出一条对称轴方程

答案

f(x)=sin(2x-2π/3)+√3(1+cos(2x-2π/3)
=√3+sin(2x-2π/3)+√3cos(2x-2π/3)
=√3+2sin(2x-π/3)
1)2x-π/3=2kπ+π/2,即x=kπ+5π/12,fmax=√3+2
2x-π/3=2kπ-π/2,即x=kπ-π/12,fmax=√3-2
2)对称轴即为x取最大值或最小值时的点,比如：x=5π/12