Question

In an isosceles right angled triangle $ABC$, a value of $\tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right)$ is

• A. $\sqrt{2}-1$
• B. $2\sqrt{2}$
• C. $2\sqrt{2}-1$
• D. $2\sqrt{2}+1$

Answer 1

Answer: (C)

$2\sqrt{2}-1$

Answer 2

Given, an isosceles right angled triangle ABC.Then, $\angle A=\angle C={{45}^{o}}$ and $\angle B={{90}^{o}}$
Now, $\tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right)$
$=\tan \left( \frac{{{45}^{o}}}{2} \right)+\tan \left( \frac{{{90}^{o}}}{2} \right)+\tan \left( \frac{{{45}^{o}}}{2} \right)$
$=\sqrt{2}-1+1+\sqrt{2}-1$ $\left[ \because \,\,\,\tan \left( {{22}^{o}}\frac{1}{2} \right)=\sqrt{2}-1 \right]$
$=2\sqrt{2}-1$