设 $\alpha \in\left(0, \frac{\pi}{2}\right), \beta \in\left(0, \frac{\pi}{2}\right)$, 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
$2 \alpha+\beta=\frac{\pi}{2}$
E
F