Question

Let ∆ = $\left| \begin{matrix} 1 & \sin\theta & 1 \\ –\sin\theta & 1 & \sin\theta \\ –1 & –\sin\theta & 1 \end{matrix} \right|$, then minimum & maximum

values of ∆ are –

• A. 2, 3
• B. 3, 4
• C. 2, 4
• D. None of these

Answer 1

Answer: (C)

2, 4

Answer 2

Q∆ = +1 (1 + sin²θ) – sinθ (0) + 1 (1 + sin²θ)

∴∆ = 2 + 2 sin² θ

∆_min (when sin θ = 0) = 2 & ∆_max (when sin θ = 1) = 2 + 2 = 4.