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Given that cot(theta) + cosec(theta) = 5, find cos(theta).

1. 12/13
2. 5/13
3. 13/12
4. 1/5

Correct answer: 12/13

Solution

From the pair cosec + cot = 5 and cosec - cot = 1/5, solving gives cosec = 13/5 and cot = 12/5, so cos = cot/cosec = 12/13.

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