Question

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