Question

The value of $\tan\left\lbrack \sin^{- 1}\left( \frac{3}{5} \right) + \cos^{- 1}\left( \frac{3}{\sqrt{13}} \right) \right\rbrack$ is

• A. $\frac{6}{17}$
• B. $\frac{6}{\sqrt{13}}$
• C. $\frac{\sqrt{13}}{5}$
• D. $\frac{17}{6}$

Answer 1

Answer: (D)

$\frac{17}{6}$

Answer 2

$\mathbf{\tan}\left\lbrack \mathbf{\sin}^{\mathbf{- 1}}\left( \frac{\mathbf{3}}{\mathbf{5}} \right)\mathbf{+}\mathbf{\cos}^{\mathbf{- 1}}\left( \frac{\mathbf{3}}{\sqrt{\mathbf{13}}} \right) \right\rbrack$ = $\tan\left( \tan^{- 1}\frac{3}{4} + \tan^{- 1}\frac{2}{3} \right)$

= $\tan\left( \tan^{- 1}{}\frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3}{4}.\frac{2}{3}} \right)$ = $\tan\left\lbrack \tan^{- 1}\frac{17}{12} \times \frac{12}{6} \right\rbrack$ = $\frac{17}{6}$