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)

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