The value of $\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)$ is equal to

• A

  $0$
• Correct answer
  B

  $\frac{\pi}{4}$
• C

  $\frac{\pi}{3}$
• D

  $\frac{\pi}{2}$

Solution

$\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)$
$\sin \theta=\frac{3}{5}$ $\begin{aligned} & \tan \theta=\frac{3}{4} \\ & =\tan ^{-1}\left(\frac{3}{4}\right)+\tan ^{-1}\left(\frac{1}{7}\right)\end{aligned}$ $=\tan ^{-1}\left(\frac{\frac{3}{4}+\frac{1}{7}}{1-\frac{3}{4} \cdot \frac{1}{7}}\right)$ $=\tan ^{-1}\left(\frac{\frac{21+4}{28}}{\frac{28-3}{28}}\right)$ $=\tan ^{-1}\left(\frac{25}{25}\right)=\tan ^{-1}(1)=\frac{\pi}{4}$

Hence, the correct answer is option: 'B'.