ત્રિકોણમિતીય પ્રતિવિધેયો — ગણિત ધોરણ 12 સાયન્સ — Question

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