Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

If $b+c=3a$ then $\cot \frac{B}{2}\cdot \cot \frac{C}{2}$ has the value equal to?

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (C)

$2$

Given $b+c=3a$
We know $a+b+c=2s$
$\Rightarrow s=2a$

Consider, $\cot \frac{B}{2}.\cot \frac{C}{2}$
$=\sqrt{\frac{\left(s\right)(s-b)}{(s-a)(s-c)}.\frac{\left(s\right)(s-c)}{(s-a)(s-b)}}$
$=\frac{s}{s-a}=2$