1. The problem is to simplify the expression $$\frac{\cos A}{1-\tan A} + \frac{\sin A}{1-\cot A}$$. 2. Recall that $$\tan A = \frac{\sin A}{\cos A}$$ and $$\cot A = \frac{\cos A}{\sin A}$$. 3. Substitute these into the expression: $$\frac{\cos A}{1 - \frac{\sin A}{\cos A}} + \frac{\sin A}{1- \frac{\cos A}{\sin A}}$$. 4. Simplify the denominators: $$1 - \frac{\sin A}{\cos A} = \frac{\cos A - \sin A}{\cos A}$$, $$1 - \frac{\cos A}{\sin A} = \frac{\sin A - \cos A}{\sin A}$$. 5. Rewrite the original expression with these: $$\frac{\cos A}{\frac{\cos A - \sin A}{\cos A}} + \frac{\sin A}{\frac{\sin A - \cos A}{\sin A}} = \frac{\cos A \cdot \cos A}{\cos A - \sin A} + \frac{\sin A \cdot \sin A}{\sin A - \cos A}$$. 6. This becomes: $$\frac{\cos^2 A}{\cos A - \sin A} + \frac{\sin^2 A}{\sin A - \cos A}$$. 7. Note that $$\sin A - \cos A = -(\cos A - \sin A)$$, so rewrite second term: $$\frac{\cos^2 A}{\cos A - \sin A} - \frac{\sin^2 A}{\cos A - \sin A} = \frac{\cos^2 A - \sin^2 A}{\cos A - \sin A}$$. 8. Recognize numerator as $$\cos 2A$$ identity: $$\cos^2 A - \sin^2 A = \cos 2A$$. 9. The expression now is: $$\frac{\cos 2A}{\cos A - \sin A}$$. **Final answer:** $$\frac{\cos 2A}{\cos A - \sin A}$$.