Question

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 maximum and minimum values of \( f(\theta) \). Then \( (A,B) \) is:

• A. \( (2,1) \)
• B. \( (2,0) \)
• C. \( (\sqrt{2},1) \)
• D. \( (2,\frac{1}{\sqrt{2}}) \)

Hint:

For trig determinants:

• Expand carefully.
• Reduce to sine/cosine bounds.

Answer 1

The Correct Option is B