先化简,就比较容易看出来了
f(x)=sin(x+π/4)+sin(π/4-x)
=sinxcos(π/4)+cosxsin(π/4)+sin(π/4)cosx-cos(π/4)sinx
=2cosxsin(π/4)
=√2cosx
∴ f(-x)=√2cos(-x)=√2cosx=f(x)
∴ f(x)是偶函数
另法：
直接做也可以
f(x)=sin(x+π/4)+sin(π/4-x)
f(-x)=sin(-x+π/4)+sin(π/4+x)
=sin(x+π/4)+sin(π/4-x)
=f(x)
∴ f(x)是偶函数.