Question

$\cos \left({\sin }^{-1}\left(\tan \left({\cos }^{-1}\left(\sin \left({\tan }^{-1}\frac{4}{3}\right)\right)\right)\right)\right)$ is equal to

• A. $\frac{3}{5}$
• B. $\frac{\sqrt{7}}{4}$
• C. $\frac{3}{4}$
• D. $\frac{4}{5}$

Answer 1

The correct option is B $\frac{\sqrt{7}}{4}$

The value of $\cos \left({\sin }^{-1}\left(\tan \left({\cos }^{-1}\left(\frac{4}{5}\right)\right)\right)\right)$
$=\cos \left({\sin }^{-1}\left(\tan \left({\tan }^{-1}\left(\frac{3}{4}\right)\right)\right)\right)$
$=\cos \left({\sin }^{-1}\left(\frac{3}{4}\right)\right)=\cos \left({\cos }^{-1}\left(\frac{\sqrt{7}}{4}\right)\right)=\frac{\sqrt{7}}{4}$