Question

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

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

Answer 1

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

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

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

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

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

$=\cos {\sin }^{-1}\frac{3}{4}$

$=\cos {\cos }^{-1}\frac{\sqrt{7}}{4}$

$=\frac{\sqrt{7}}{4}$