The value of $tan \begin{Bmatrix} 2 tan^{-1} \left(\frac{1}{5}\right) + \frac{\pi}{4}\end{Bmatrix}$ is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{17}{7}$
$\tan\left\{2 \tan^{-1} \left(\frac{1}{5}\right) + \frac{\pi}{4}\right\}$
$2 \tan^{-1}\frac{1}{5}=\tan^{-1}\left(\frac{2×\frac{1}{5}}{1-(\frac{1}{5})^2}\right)$
$\tan^{-1}\left(\frac{10}{24}\right)=\tan^{-1}\frac{5}{12}$
$=\tan\left(\tan^{-1}\frac{5}{12}+\tan^{-1}\right)$
$=\frac{\frac{5}{12}+1}{1-\frac{5}{12}}=\frac{17}{7}$