Question

Which is greater $\tan 1$ or ${\tan }^{-1}$ ?

Answer 1

We know, ${\tan }^{-1}1=\frac{\pi }{4}$ and $1>\frac{\pi }{4}$

Now,

$1>\frac{\pi }{4}$

$\tan 1>\tan \frac{\pi }{4}$

$\tan 1>1$

$\tan 1>1>\frac{\pi }{4}$

$\tan 1>{\tan }^{-1}1$