Trigonometric Equations Question 152
Question: In any triangle ABC, $ a\cot A+b\cot B+c\cot C= $
Options:
A) $ r+R $
B) $ r-R $
C) $ 2(r+R) $
D) $ 2(r-R) $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ a\cot A+b\cot B+c\cot C $ = $ 2R(\sin A\cot A+\sin B\cot B+\sin C\cot C) $ = $ 2R(\cos A+\cos B+\cos C) $ = $ 2R( 1+4\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2} )=2R( 1+\frac{r}{R} )=2,(R+r) $ .
BETA
