Question

The value of $\tan \left(2{\tan }^{-1}\left(\frac{3}{5}\right)+{\sin }^{-1}\left(\frac{5}{13}\right)\right)$ is equal to :

• A. $\frac{-181}{69}$
• B. $\frac{220}{21}$
• C. $\frac{-291}{76}$
• D. $\frac{151}{63}$

Answer 1

Answer: (B)

${\tan }^{-1}\frac{3}{5}+{\tan }^{-1}\frac{3}{5}+{\tan }^{-1}\frac{5}{12}$
${\tan }^{-1}\frac{\frac{6}{5}}{1-\frac{9}{25}}={\tan }^{-1}\frac{15}{8}+{\tan }^{-1}\frac{5}{12}$
${\tan }^{-1}\frac{\frac{15}{8}+\frac{5}{12}}{1-\frac{15}{8}\cdot \frac{5}{12}}={\tan }^{-1}\frac{220}{21}$
$\tan \left({\tan }^{-1}\frac{220}{21}\right)=\frac{220}{21}$