Trigonometric Equations Question 312
Question: Which of the following is true in a triangle ABC
[IIT Screening 2005]
Options:
A) $ (b+c)\sin \frac{B-C}{2}=2a\cos \frac{A}{2} $
B) $ (b+c)\cos \frac{A}{2}=2a\sin \frac{B-C}{2} $
C) $ (b-c)\cos \frac{A}{2}=a\sin \frac{B-C}{2} $
D) $ (b-c)\sin \frac{B-C}{2}=2a\cos \frac{A}{2} $
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Answer:
Correct Answer: C
Solution:
- $ \frac{b-c}{a}=\frac{\sin B-\sin C}{\sin A}=\frac{2\sin \frac{B-C}{2}\cos \frac{B+C}{2}}{2\sin \frac{A}{2}\cos \frac{A}{2}}=\frac{\sin \frac{B-C}{2}}{\cos \frac{A}{2}} $
Þ $ (b-c)\cos \frac{A}{2}=a\sin \frac{B-C}{2} $ .
BETA
