Question

If in a $△ABC,3a=b+c$, then the value of $\cos \frac{B}{2}\cot \frac{C}{2}$

• A. $1$
• B. $\sqrt{3}$
• C. $2$
• D. None of the above

Answer 1

The correct option is C $2$

Mistake :$\cot \frac{B}{2}$ must be there instead of $\cos \frac{B}{2}$

$b+c=3a$

$2s=a+b+c=a+3a=4a⟹s=2a$

$s-a=2a-a=a$

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