题目

已知函数f(x)=sin(x+π/6)+sin(x-π/6)+cosx,则函数f(x)图像的对称轴为

提问时间：2020-08-01

答案

f(x)=sinxcosπ/6+cosxsinπ/6+sinxcosπ/6-cosxsinπ/6+cosx
=sinx+cosx
=√2sin(x+π/4)
对称轴则sin(x+π/4)=±1
x+π/4=kπ+π/2
所以是x=kπ+π/4