[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) $\tan \left[2 \tan ^{-1}\left(\frac{1}{5}\right)-\frac{\pi}{4}\right]$
$=\tan \left[\tan ^{-1} \frac{\frac{2}{5}}{1-\frac{1}{25}}-\tan ^{-1}(1)\right]$
$=\tan \left[\tan ^{-1} \frac{5}{12}-\tan ^{-1}(1)\right]$
$=\tan \left[\tan ^{-1}\left(\frac{\frac{5}{12}-1}{1+\frac{5}{12}}\right)\right]$
$=-\frac{7}{17}$

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