Question

In $\Delta ABC$ if $\tan \frac{C}{2}$ $(atanA+btanB)=a+b$, then the triangle is

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

Answer 1

The correct option is B isosceles

On checking respectively, we can see that

$\tan \frac{c}{2}=a$ on the RHS

and the other section which involves the $\tan$ and their corresponding sides being equal to each other, when we equate it to ${}^{\prime }{b}^{\prime }$.

We can thus conclude that sides $a$ and $b$ are equal, while $c$ has a different value.

Thus $△ABC$ is an isosceles triangle.