Question

The value of the determinant \[ \begin{vmatrix} \cos(\alpha - \beta) & \cos \alpha & \cos \beta
\cos(\alpha - \beta) & 1 & \cos \beta
\cos \alpha & \cos \beta & 1 \end{vmatrix} \]

• A. \( \alpha^2 + \beta^2 \)
• B. \( \alpha^2 - \beta^2 \)
• C. \( 1 \)
• D. None of these

Hint:

To solve matrix determinants, use cofactor expansion or row/column operations.

Answer 1

The Correct Option is D

Step 1: Evaluating the determinant.
To evaluate this determinant, apply cofactor expansion. The value of the determinant simplifies to \( \alpha^2 - \beta^2 \).

Step 2: Conclusion.
The correct answer is \( \alpha^2 - \beta^2 \), corresponding to option (2).