[ 2 ^ - 1 ( 1 5 ) - 4 ] = - Vidyadip

MCQ

$\tan \left[ {2{{\tan }^{ - 1}}\left( {\frac{1}{5}} \right) - \frac{\pi }{4}} \right] = $

A
$\frac{{17}}{7}$
B
$ - \frac{{17}}{7}$
C
$\frac{7}{{17}}$
✓
$ - \frac{7}{{17}}$

✓

Answer

Correct option: D.

$ - \frac{7}{{17}}$

d
(d) $\tan \left[ {2{{\tan }^{ - 1}}\left( {\frac{1}{5}} \right) - \frac{\pi }{4}} \right] = \tan \left[ {{{\tan }^{ - 1}}\frac{{\frac{2}{5}}}{{1 - \frac{1}{{25}}}} - {{\tan }^{ - 1}}(1)} \right]$

$ = \tan \left[ {{{\tan }^{ - 1}}\frac{5}{{12}} - {{\tan }^{ - 1}}(1)} \right] = \tan {\tan ^{ - 1}}\left( {\frac{{\frac{5}{{12}} - 1}}{{1 + \frac{5}{{12}}}}} \right) = - \frac{7}{{17}}$.

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