Question

The numerical value of tan $\left[2ta{n}^{-1}\right(\frac{1}{5})-\frac{\pi }{4}]$is...

Answer 1

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