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If the minimum and the maximum values of the function f : [π/4, π/2] → R, defined by: f(θ) = | -sin^2 θ -1 - sin^2 θ 1 | | -cos^2 θ -1 - cos^2 θ 1 | | 12 10 -2 | are m and M respectively, then the ordered pair (m, M) is equal to :

1. (0, 4)
2. (-4, 4)
3. (0, 2√2)
4. (-4, 0)

Correct answer: (-4, 4)

Solution

The function evaluates to a determinant that depends on the values of sin²θ and cos²θ, which vary between 0 and 1 in the given interval. By calculating the determinant at the endpoints of the interval, we find that the minimum value is -4 and the maximum value is 4, confirming that the ordered pair (m, M) is (-4, 4).

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