Question

In a $△ABC$ if $b+c=3a$, then $\cot \frac{B}{2}.\cot \frac{C}{2}$ has the value equal to

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$\cot \frac{B}{2}\cdot \cot \frac{C}{2}$

we know,

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

$\therefore \cot \frac{B}{2}\cdot \cot \frac{C}{2}=\frac{s}{s-a}$

$s=\frac{a+b+c}{2}\Rightarrow \frac{a+3a}{2},s=2a$

$\cot \frac{B}{2}\cdot \cot \frac{C}{2}=\frac{2a}{2a-a}\Rightarrow 2$