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Determine the minimum value of the expression 4*sec²(x) + 9*cosec²(x).

1. 25
2. 13
3. 36
4. 30

Correct answer: 25

Solution

Expanding gives 13 + 4*tan²(x) + 9*cot²(x); by AM-GM, 4*tan² + 9*cot² >= 2*sqrt(36) = 12, so the minimum is 13 + 12 = 25.

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