Answer:
Option B
Explanation:
Given expression is
$\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$
= $\frac{\sin A}{\cos A}\times\frac{\sin A}{\sin A-\cos A}+\frac{\cos A}{\sin A}\times\frac{\cos A}{\cos A-\sin A}$
= $\frac{1}{\sin A-\cos A}\left\{\frac{\sin^{3}A-\cos^{3} A}{\cos A\sin A}\right\}$
= $\frac{\sin^{2}A+\sin A \cos A+\cos^{2} A}{\cos A\sin A}$
= $\frac{1-\sin A \cos A}{\cos A\sin A}$
=1+ sec A cosec A
