WBJEE · Maths · Determinants
Let \(f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right|\). Suppose \(A\) and \(B\) are respectively maximum and minimum values of \(f(\theta)\). Then \((A, B)\) is equal to
- A \((2,1)\)
- B \((2,0)\)
- C \((\sqrt{2}, 1)\)
- D \(\left(2, \frac{1}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(B) \((2,0)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right| \text { (after expansion) } \\ & f(\theta)=1+\sin 2 \theta \\ & A=2, B=0 \quad(A, B)=(2,0)\end{aligned}\)
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