Sorry for asking so many of these type of questions.
How would I verify the following trigonometry identity:
$\frac{\sin A+\tan A}{\cot A+\csc A}=\sin A \tan A.$
My work is
$\frac{\sin A + \frac{\sin A}{\cos A}}{\frac{\cos A}{\sin A} + \frac{1}{\sin A}}.$
Do I have to use a common denominator between the sin and tan to solve the identity?