Search any question & find its solution
Question:
Answered & Verified by Expert
If, in a $\triangle A B C, \tan \frac{A}{2}=\frac{5}{6}$ and $\tan \frac{C}{2}=\frac{2}{5}$, then $a, b, c$ are such that :
Options:
Solution:
2919 Upvotes
Verified Answer
The correct answer is:
$2 b=a+c$
$\because \quad \tan A=\frac{5}{6}$ and $\tan C=\frac{2}{5}$
$\therefore \quad \tan A \tan C=\frac{5}{6} \cdot \frac{2}{5}$
$\Rightarrow \quad \frac{s-b}{s}=\frac{1}{3}$
$\Rightarrow \quad 3 s-3 b=s$
$\Rightarrow \quad 2 s=3 b$
$\Rightarrow \quad a+c=2 b$
$\therefore \quad \tan A \tan C=\frac{5}{6} \cdot \frac{2}{5}$
$\Rightarrow \quad \frac{s-b}{s}=\frac{1}{3}$
$\Rightarrow \quad 3 s-3 b=s$
$\Rightarrow \quad 2 s=3 b$
$\Rightarrow \quad a+c=2 b$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.