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The value of the determinant $Δ = \begin{vmatrix}sin 2\alpha & sin ( \alpha + \beta) & sin (\alpha + \gamma )\\sin (\beta + \gamma ) & sin 2 \beta & sin (\gamma + \beta)\\(sin \gamma + \alpha ) & sin ( \gamma + \beta ) & sin 2 \gamma \end{vmatrix},$ is |
0 $sin^2\alpha + sin^2 \beta + sin^2 \gamma $ $\frac{3}{2}$ none of these |
0 |
The correct answer is option (1) : 0 We have, $Δ=\begin{vmatrix}sin \alpha & cos \alpha &0 \\sin \beta & cos\beta & 0\\sin \gamma & cos \gamma & 0\end{vmatrix}\begin{vmatrix}cos\alpha & sin\alpha &0 \\cos\beta & sin\beta & 0\\cos\gamma & sin\gamma & 0\end{vmatrix}$ $⇒Δ=0×0=0$ |
