Question

If A, B, C are the angle of a triangle then the value of

determinant $\left| \begin{matrix} \sin 2A & \sin C & \sin B \\ \sin C & \sin 2B & \sin A \\ \sin B & \sin A & \sin 2C \end{matrix} \right|$ is –

• A. π
• B. 2π
• C. 0
• D. None of these

Answer 1

Answer: (C)

0

Answer 2

$\left| \begin{matrix} \sin 2A & \sin C & \sin B \\ \sin C & \sin 2B & \sin A \\ \sin B & \sin A & \sin 2C \end{matrix} \right|$

= $\left| \begin{array} { l l l } \sin A & \cos A & 0 \\ \sin B & \cos B & 0 \\ \sin C & \cos C & 0 \end{array} \right|$ $\left| \begin{matrix} \cos A & \sin A & 0 \\ \cos B & \sin B & 0 \\ \cos C & \sin C & 0 \end{matrix} \right|$= 0