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Find the maximum and minimum values of the expression 9 cos² x + 48 sin x cos x - 5 sin² x - 2.

1. Maximum 25, minimum -25
2. Maximum 23, minimum -27
3. Maximum 27, minimum -23
4. Maximum 20, minimum -30

Correct answer: Maximum 25, minimum -25

Solution

The expression simplifies to 7 cos 2x + 24 sin 2x (the constants cancel), whose amplitude is 25, so the range is [-25, 25].

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