A) \[2\sin \alpha \sin \beta \sin \gamma \]
B) \[4\sin \alpha \sin \beta \sin \gamma \]
C) \[\sin \alpha \sin \beta \sin \gamma \]
D) None of these
Correct Answer: B
Solution :
Combine first two terms and last two terms L.H.S.\[=2\,\sin \gamma \cos \,(\beta -\alpha )+2\,\sin \,(-\gamma )\,\cos \,(\alpha +\beta )\] \[=2\,\sin \,\gamma \,[\cos \,(\beta -\alpha )-\cos \,(\alpha +\beta )]\] \[=2\,\sin \,\gamma \,.\,2\,\sin \alpha \,\sin \beta \]\[=4\sin \alpha \sin \beta \sin \gamma \].
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