已知函数f(x)=sin(4x+π/4+cos(4x-π/4)若直线x=m是函数f(x)对称轴,求实数m的值

已知函数f(x)=sin(4x+π/4+cos(4x-π/4)若直线x=m是函数f(x)对称轴,求实数m的值
已知函数f(x)=sin(4x+π/4+cos(4x-π/4)若直线x=m是函数f(x)对称轴,求实数m的值

已知函数f(x)=sin(4x+π/4+cos(4x-π/4)若直线x=m是函数f(x)对称轴,求实数m的值
由cosα = sin（π/2+α）,得
f(x)=sin(4x+π/4）+cos(4x-π/4)
=sin(4x+π/4）+sin【(4x-π/4)+π/2】
=2sin(4x+π/4）
令4x+π/4=kπ+π/2,解得x=kπ/4+π/16(k∈Z)
所以m=kπ/4+π/16(k∈Z)