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...