Trigonometric-Identities Question 392
Question: $ \sin (\beta +\gamma -\alpha )+\sin (\gamma +\alpha -\beta ) $ $ +\sin (\alpha +\beta -\gamma )-\sin (\alpha +\beta +\gamma )= $
Options:
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
Show Answer
Answer:
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 $ .
BETA
