A) \[\sin C,\sin \frac{A}{2}\]
B) \[\cos C,\sin \frac{A}{2}\]
C) \[\sin C,\cos \frac{A}{2}\]
D) None of these
Correct Answer: B
Solution :
\[\sqrt{\frac{b+c}{4c}}=\sqrt{\frac{\sin 3C+\sin C}{4\sin C}}\] Þ \[\sqrt{\frac{2\sin 2C\cos C}{4\sin C}}=\cos C\] \[\frac{b-c}{2c}=\frac{\sin 3C-\sin C}{2\sin C}=\frac{2\cos 2C\sin C}{2\sin C}=\cos 2C=\sin \frac{A}{2}\].
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