Question

In $\Delta$ABC , if cot $\frac{A}{2}=\frac{B+C}{a}$ then $\Delta$ABC must be

• A. isosceles
• B. equilatteral
• C. right angle
• D. right angle isosceles

Answer 1

Answer: (C)

right angle

$\frac{cos\frac{A}{2}}{sin\frac{A}{2}}=\frac{sinB+sinC}{sinA}$
$\frac{cos\frac{A}{2}}{sin\frac{A}{2}}=\frac{2sin\frac{B+C}{2}+cos\frac{B-C}{2}}{2sin\frac{A}{2}cos\frac{A}{2}}$
$cos\frac{A}{2}=cos\left(\frac{B-C}{2}\right)$
$A=B-C\Rightarrow A+C=B$
$\angle B=\frac{\pi }{2}$