Trigonometric Equations Question 217
Question: In $ \Delta ABC $ , if $ \tan \frac{A}{2}\tan \frac{C}{2}=\frac{1}{2}, $ then $ a,b,c $ are in
Options:
A) A. P.
B) G. P.
C) H. P.
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ \tan \frac{A}{2}\tan \frac{C}{2}=\frac{r}{s} $
Þ $ \sqrt{\frac{(s-b)(s-c)}{s(s-a)}\frac{(s-a)(s-b)}{s(s-c)}}=\frac{1}{2} $
Þ $ \frac{s-b}{s}=\frac{1}{2}\Rightarrow 2s-2b-s=0 $
Þ $ a+c-3b=0 $ .
BETA
