Trigonometric Equations Question 205
Question: In $ \Delta ABC, $ a $ \sin (B-C)+b\sin (C-A)+c\sin (A-B)= $
[ISM Dhanbad 1973]
Options:
A) 0
B) $ a+b+c $
C) $ a^{2}+b^{2}+c^{2} $
D) $ 2(a^{2}+b^{2}+c^{2}) $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ a\sin (B-C)+b\sin (C-A)+c\sin (A-B) $ $ =k,(\Sigma \sin A\sin (B-C) $ $ =k,{\Sigma \sin (B+C)\sin (B-C)} $ $ =k,{ \Sigma \frac{1}{2}(\cos 2C-\cos 2B) }=0 $ . Note: Students should note here that most of the expressions containing the cyclic factor associating with ?-? reduces to 0.
BETA
