设 $\alpha \in (0,\frac{\pi }{2}),\beta \in (0,\frac{\pi }{2})$且 $\tan \alpha =\frac{1+\sin \beta }{\cos \beta }$则（   ）

A．

$3\alpha -\beta =\frac{\pi }{2}$

B．

$3\alpha +\beta =\frac{\pi }{2}$

C．

$2\alpha -\beta =\frac{\pi }{2}$

D．

$2\alpha +\beta =\frac{\pi }{2}$