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Find the minimum value of cos(theta) + cos(2*theta) over all real theta.

1. -9/8
2. -2
3. -1
4. -3/2

Correct answer: -9/8

Solution

Substituting x = cos theta gives a quadratic 2x² + x - 1 whose minimum on [-1,1] is at x = -1/4, value -9/8.

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