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Simplify the expression cos A/(1 - tan A) + sin A/(1 - cot A).

1. sin A + cos A
2. sin A - cos A
3. 1
4. sin A * cos A

Correct answer: sin A + cos A

Solution

Rewriting each term over a common sine/cosine form gives cos² A/(cos A - sin A) - sin² A/(cos A - sin A) = (cos² A - sin² A)/(cos A - sin A) = cos A + sin A.

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