Evaluate: 2 ^ -1 (1 5 ) + 4 - Vidyadip

Question

Evaluate:
$\tan\Bigg\{ 2\tan ^{-1} \bigg(\frac{1}{5}\bigg) + \frac{\pi}{4}\Bigg\}$

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Answer

$\tan\Bigg\{\tan^{-1}\bigg(\frac{1}{5}\bigg) + \frac{\pi}{4}\Bigg\} = \tan \Bigg\{\tan^{-1} \Bigg(\frac{2/5}{1 - \frac{1}{25}}\Bigg) + \frac{\pi}{4}\Bigg\}$
$= \tan \Bigg\{\tan^{-1} \bigg(\frac{5}{12}\bigg) + \frac{\pi}{4}\Bigg\}$
$\frac{\frac{5}{12}+1}{1 - \frac{5}{12}} = \frac{17}{7}$

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