$\dfrac{\cos A}{1-\tan A} + \dfrac{\sin A}{1 - \cot A}$is equal to

Simplifying the above equation we get

$\dfrac{\cos A}{1-\tan A}+\dfrac{\sin A}{1-cotA}$

$=\dfrac{\cos A}{1-\dfrac{\sin A}{\cos A}}+\dfrac{\sin A}{1-\dfrac{\cos A}{\sin A}}$

$=\dfrac{\cos ^2A}{\cos A-\sin A}+\dfrac{\sin ^2A}{\sin A-\cos A}$

$=\dfrac{\cos ^2A-\sin ^2A}{\cos A-\sin A}$

$=\dfrac{(\cos A-\sin A)(\cos A+\sin A)}{\cos A-\sin A}$

$=\cos A+\sin A$

Hence answer is B