Question

In $\Delta ABC,$ if $\left(\tan \frac{C}{2}\right).(a\tan A+b\tan B)=a+b,$ then triangle is

• A. Right angled
• B. Isosceles
• C. Equilateral
• D. Obtuse angled

Answer 1

Answer: (B)

Isosceles

If $\tan \frac{C}{2}\cdot (a\tan A+b\tan B)=a+b$

So here, if we check respectively $\tan \frac{C}{2}=a$ and the other part where the $\tan$ and their corresponding sides are equal as they equate to ${}^{\prime }{b}^{\prime }$ shows that $△ABC$ is an isosceles triangle.