Question

The value of $\tan \{{\cos }^{-1}\left(\frac{4}{5}\right)+{\sin }^{-1}\left(\frac{2}{\sqrt{13}}\right)\}$ is

• A. $\frac{-7}{16}$
• B. $\frac{17}{6}$
• C. $\frac{6}{17}$
• D. none of these

Answer 1

Answer: (B)

$\frac{17}{6}$

Given, $\tan \{{\cos }^{-1}\left(\frac{4}{5}\right)+{\sin }^{-1}\left(\frac{2}{\sqrt{13}}\right)\}$
$=\tan \{{\tan }^{-1}\left(\frac{3}{4}\right)+{\tan }^{-1}\left(\frac{2}{3}\right)\}$
$=\tan \left\{{\tan }^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}\times \frac{2}{3}}\right)\right\}$
$=\tan \left\{{\tan }^{-1}\left(\frac{17}{6}\right)\right\}=\frac{17}{6}$