Question

Evaluate :

$\tan \left(2{\tan }^{-1}\frac{1}{5}\right)$

• A. $\frac{5}{6}$
• B. $\frac{5}{12}$
• C. $\frac{7}{12}$
• D. none of these
  

Answer 1

The correct option is B $\frac{5}{12}$

$\tan \left(2{\tan }^{-1}\frac{1}{5}\right)=\tan \left[{\tan }^{-1}\right(\frac{2\times 1/5}{1-1/25}]=\tan ({\tan }^{-1}\frac{5}{12})=\frac{5}{12}$