# How do you prove  (sin A + tan A) / (1+ cos A) = tan A?

$\frac{\sin A + \sin \frac{A}{\cos A}}{1 + \cos A} =$
$\frac{\sin A . \cos A + \sin A}{\cos A \left(1 + \cos A\right)} =$
$= \frac{\sin A \left(1 + \cos A\right)}{\cos A \left(1 + \cos A\right)} = \sin \frac{A}{\cos A} = \tan A$