Question

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

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

Answer 1

Answer: (C)

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