Question

If \(c = 2\cos\theta\), then the value of the determinant \(\Delta = \begin{vmatrix} c & 1 & 0 \\ 1 & c & 1 \\ 6 & 1 & c \end{vmatrix}\) is

• A. \(\frac{\sin 4\theta}{\sin\theta}\)
• B. \(\frac{2\sin^2 2\theta}{\sin\theta}\)
• C. \(4\cos^2\theta(2\cos\theta - 1)\)
• D. None of these

Hint:

Use determinant expansion formula: \(|A| = a_{11}(a_{22}a_{33} - a_{23}a_{32}) - a_{12}(a_{21}a_{33} - a_{23}a_{31}) + a_{13}(a_{21}a_{32} - a_{22}a_{31})\).

Answer 1

The Correct Option is D