Trigonometric Equations Question 99
Question: In a $ \Delta ABC, $ if $ (\sin A+\sin B+\sin C) $ $ (\sin A+\sin B-\sin C) $ = $ 3\sin A\sin B, $ then the angle C is equal to
[AMU 1999]
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ (a+b+c)(a+b-c)=3ab $
Þ $ \frac{a^{2}+b^{2}-c^{2}}{2ab}=\frac{1}{2}\Rightarrow \cos C=\cos \frac{\pi }{3}\Rightarrow \angle C=\pi /3 $
BETA
