Bài giải:

$\frac{\cos \alpha -\sin \alpha }{\cos \alpha +\sin \alpha }=\frac{\cos \alpha -\sin \alpha }{\cos \alpha }:\frac{\cos \alpha +\sin \alpha }{\cos \alpha }$

$=\left( \frac{\cos \alpha }{\cos \alpha }-\frac{\sin \alpha }{\cos \alpha } \right):\left( \frac{\cos \alpha }{\cos \alpha }+\frac{\sin \alpha }{\text{cos}\alpha } \right)$

$=(1-\tan \alpha ):(1+\tan \alpha )=(1-\frac{1}{3}):(1+\frac{1}{3})=\frac{2}{3}:\frac{4}{3}=\frac{1}{2}$