Question

Find which of the following given numbers is greater (189-191).
tan 1 or ${\tan }^{-1}$?

Answer 1

We know that $1rad\approx {57.3}^o>{45}^o$

$⟹\tan 1>\tan {45}^o=1$

$⟹\tan 1>1$

Now, $arctan1={\tan }^{-1}1=\frac{\pi }{4}<1$

Hence,

$\tan 1>arctan1$