Question

In $△ABC,\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$ is equal to

• A. $\frac{△}{r^2}$
• B. $\frac{{(a+b+c)}^2}{abc}2R$
• C. $\frac{△}{r}$
• D. $\frac{△}{Rr}$

Answer 1

The correct option is A $\frac{△}{r^2}$

Hence

$cot\frac{A}{2}+cot\frac{B}{2}+cot\frac{C}{2}$

$=\frac{s-a}{r}+\frac{s-b}{r}+\frac{s-c}{r}$

$=\frac{1}{r}\left[\right(2s-(a+b+c))+s]$
$=\frac{s}{r}$
$=\frac{△}{r^2}$.