$\frac{\sin \alpha }{\cos \alpha }+\frac{\cos \alpha }{\sin \alpha }=2\mid \cdot \sin \alpha \cos \alpha$  

 

$\underset{1}{\underbrace{{\sin }^2\alpha +{\cos }^2\alpha }}=2\sin \alpha \cos \alpha$   

 

$1=2\sin \alpha \cos \alpha \mid :2$  

 

$\underline{\frac{1}{2}=\sin \alpha \cdot \cos \alpha }$