Question
Which is greater, tan $1$ or $\tan ^{-1} 1 ?$
✓
Answer
From Fig. we note that \tan x is an increasing function in the interval $1\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$,
since $1;\frac{\pi}{4} \Rightarrow \tan 1;\tan \frac{\pi}{4}$. This gives
$\tan 1;1$
$\Rightarrow \tan 1;1;\frac{\pi}{4}$
$\Rightarrow \tan 1;1;\tan ^{-1}(1)$
since $1;\frac{\pi}{4} \Rightarrow \tan 1;\tan \frac{\pi}{4}$. This gives
$\tan 1;1$
$\Rightarrow \tan 1;1;\frac{\pi}{4}$
$\Rightarrow \tan 1;1;\tan ^{-1}(1)$
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