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[2020] Let m and M be respectively the minimum and maximum values of the determinant [cos² x, 1+sin² x, sin 2x; 1+cos² x, sin² x, sin 2x; cos² x, sin² x, 1+sin 2x]. Then the ordered pair (m, M) is equal to -

1. (-3, -1)
2. (1, 3)
3. (-3, 3)
4. (-4, -1)

Correct answer: (-3, -1)

Solution

Expanding the determinant gives a value ranging over [-3,-1] as x varies, so (m,M)=(-3,-1).

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