f(x)=sin(x+y)+cos(x-y),y属于(0,π),若f(x)为偶函数,则y=?

f(x)=sin(x+y)+cos(x-y),y属于(0,π),若f(x)为偶函数,则y=?
f(x)=sin(x+y)+cos(x-y),y属于(0,π),若f(x)为偶函数,则y=?

f(x)=sin(x+y)+cos(x-y),y属于(0,π),若f(x)为偶函数,则y=?
f(x)=sinxcosy+cosxsiny+cosxcosy+sinxsiny
=sinx(cosy+siny)+cosx(siny+cosy)
=(sinx+cosx)(siny+cosy)
f(-x)=(-sinx+cosx)(siny+cosy)=(sinx+cosx)(siny+cosy)
siny+cosy=0
tany=-1
y=3/4π