Question

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

• A. $\frac{12}{13}$
• B. $\frac{-12}{5}$
• C. $\frac{12}{5}$
• D. $\frac{-12}{13}$

Answer 1

The correct option is B $\frac{-12}{5}$

$\tan (2{\sin }^{-1}\frac{5}{13}+{\cos }^{-1}\frac{5}{13})$
$=\tan (\frac{\pi }{2}+{\sin }^{-1}\frac{5}{13})$
$=-\cot \left({\sin }^{-1}\frac{5}{13}\right)$
$=-\cot \left({\cot }^{-1}\frac{12}{5}\right)$
$=\frac{-12}{5}$