Trigonometric Equations Question 184
Question: Which is true in the following
[UPSEAT 1999]
Options:
A) $ a\cos A+b\cos B+c\cos C=R\sin A\sin B\sin C $
B) $ a\cos A+b\cos B+c\cos C=2R\sin A\sin B\sin C $
C) $ a\cos A+b\cos B+c\cos C=4R\sin A\sin B\sin C $
D) $ a\cos A+b\cos B+c\cos C=8R\sin A\sin B\sin C $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \because $ $ a=2R\sin A,b=2R\sin B,c=2R,\sin C $
$ \therefore $ $ a\cos A+b\cos B+c\cos C $ $ =R[(2\sin A\cos A)+(2\sin B\cos B)+(2\sin C\cos C)] $ $ =R(\sin 2A+\sin 2B+\sin 2C) $ $ =4R\sin A\sin B\sin C. $
BETA
