Question:medium
Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:
Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:
Show Hint
Simplify the expression before finding the maximum and minimum values. Utilize the range of trigonometric functions.
Updated On: Nov 28, 2025
- \( (2, 1) \)
- \( (2, 0) \)
- \( (\sqrt{2}, 1) \)
- \( \left(2, \frac{1}{\sqrt{2}}\right) \)
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