Matrix and Determinant
79460
The value of \(\sin \beta \cos \beta \sin (\beta+\gamma)\) is :
\(\sin \delta \cos \delta \sin (\gamma+\delta)\)
1 \(\sin \alpha \sin \beta \sin \delta\)
2 \(\sin \alpha \cos \beta \cos \delta\)
3 1
4 0
Explanation:
(D) :Let, \(\mathrm{D}=\left|\begin{array}{lll}\sin \alpha & \cos \alpha & \sin (\alpha+\gamma) \\ \sin \beta & \cos \beta & \sin (\beta+\gamma) \\ \sin \delta & \cos \delta & \sin (\gamma+\delta)\end{array}\right|\)
Applying \(\mathrm{C}_{3} \rightarrow \mathrm{C}_{3}-\cos \gamma \mathrm{C}_{1}-\sin \gamma \mathrm{C}_{2}\)
\(\Rightarrow \quad \mathrm{D}=\left|\begin{array}{lll}\sin \alpha & \cos \alpha & 0 \\ \sin \beta & \cos \beta & 0 \\ \sin \delta & \cos \delta & 0\end{array}\right|\)
\(\mathrm{D}=0\)