Question

Let A = $\left| \begin{matrix} 1 & \sin\theta & 1 \\ –\sin\theta & 1 & \sin\theta \\ –1 & –\sin\theta & 1 \end{matrix} \right|$, where 0 ≤θ≤2π,

then range of |A| is –

• A. (2, 4)
• B. (2, 4)
• C. (2, 4)
• D. All of these

Answer 1

Answer: (D)

All of these

Answer 2

|A| = 1 (1 + sin²θ) – sin θ (0) + 1 (sin²θ + 1) = 2 + 2sin²θ

Now as – 1 ≤ sin θ ≤ 1∴ |A| ∈ [2, 4]