Question

The value of ${lim}_{\left|x\right|\to \infty }$ $\cos \left({\tan }^{-1}\left(\sin \left({\tan }^{-1}x\right)\right)\right)$ is equal to :

• A. $-1$
• B. $\sqrt{2}$
• C. $-\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{2}}$

Given, $li{m}_{|x|\to \infty }\cos \left({\tan }^{-1}\right(\sin \left({\tan }^{-1}\right(x\left)\right)\left)\right)$

$=\cos \left({\tan }^{-1}\left(\sin \left(\frac{\pi }{2}\right)\right)\right)$ $[\tan \frac{\pi }{2}=\infty ]$

$=\cos \left({\tan }^{-1}\right(1\left)\right)$

$=\cos \left(\frac{\pi }{4}\right)$

$=\frac{1}{\sqrt{2}}$