Question

The value of $\tan \{2{\tan }^{-1}\frac{1}{5}-\frac{\pi }{4}\}$ is

• A. 0
• B. 1
• C. $\frac{7}{17}$
• D. none of these

Answer 1

Answer: (D)

none of these

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