f(x)=sin(x+y)+cos(x-y),y属于(0,π),若f(x)为偶函数,则y=?
问题描述:
f(x)=sin(x+y)+cos(x-y),y属于(0,π),若f(x)为偶函数,则y=?
答
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=0tany=-1y=3/4π