Discussion
The expression \(\frac{\sin A}{1-\cot A} + \frac{\cos A}{1-\tan A}\) can be simplified to:
Answer: C
Convert to sin and cos: \(\frac{\sin A}{1-\frac{\cos A}{\sin A}} + \frac{\cos A}{1-\frac{\sin A}{\cos A}} = \frac{\sin^2 A}{\sin A - \cos A} + \frac{\cos^2 A}{\cos A - \sin A}\)
= \(\frac{\sin^2 A}{\sin A - \cos A} - \frac{\cos^2 A}{\sin A - \cos A}\)
= \(\frac{\sin^2 A - \cos^2 A}{\sin A - \cos A}\)
= \(\frac{(\sin A - \cos A)(\sin A + \cos A)}{\sin A - \cos A} = \sin A + \cos A\).
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