Question

The value of $\tan [2{\sin }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{3}{5}]$ is

• A. $\frac{4}{3}$
• B. $-\frac{4}{3}$
• C. $\frac{3}{4}$
• D. $-\frac{3}{4}$

Answer 1

The correct option is B $-\frac{4}{3}$

$\tan [2{\sin }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{3}{5}]$
$=\tan [{\sin }^{-1}\frac{3}{5}+({\sin }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{3}{5})]$
$=\tan (\frac{\pi }{2}+{\sin }^{-1}\frac{3}{5})=-\cot \left({\sin }^{-1}\frac{3}{5}\right)=-\cot \left({\cot }^{-1}\frac{4}{3}\right)=-\frac{4}{3}$