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Find the maximum and minimum values of cos2x + cos² x.

1. max = 2, min = -1
2. max = 2, min = 0
3. max = 1, min = -1/2
4. max = 3/2, min = -1/4

Correct answer: max = 2, min = -1

Solution

The expression reduces to 3cos² x - 1, which over cos² x in [0,1] ranges from -1 to 2.

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