Cho

A

- Hướng dẫn giải

Chọn A.

Ta có: $\tan \frac{\alpha }{2}+cot\frac{\alpha }{2}=\frac{{\sin }^2{\displaystyle \frac{\alpha }{2}}+{\cos }^2{\displaystyle \frac{\alpha }{2}}}{\sin \frac{\alpha }{2}\cos \frac{\alpha }{2}}=\frac{1}{{\displaystyle \frac{1}{2}}\sin \alpha }=\frac{2}{\sin \alpha }$

Suy ra 

$\tan \frac{\alpha }{2}+cot\frac{\alpha }{2}=\frac{2}{\sin \alpha }=\frac{2}{{\displaystyle \frac{1}{\sqrt{19}}}}=2\sqrt{19}$