Question

If ∆ = $\left| \begin{matrix} 1 + \sin^{2}x & \cos^{2}x & 4\cos^{2}x \\ \sin^{2}x & 1 + \cos^{2}x & 4\sin^{2}x \\ \sin^{2}x & \cos^{2}x & 1 + 4\sin^{2}x \end{matrix} \right|$ then the

maximum value of ∆ is –

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

Answer: (B)

6

Answer 2

Apply C₁ + C₂ and then apply R₂ – R₁ and R₃ – R₁ and expand ∆ = 2 + 4 sin 2x

The maximum value of sin 2x is 1 and hence of ∆ is 6.