The function f(x) = tan x - x

The correct answer is Option (1) → always increases ##

We have, $f(x) = \tan x - x$

$∴f'(x) = \sec^2 x - 1 \quad [∵\sec^2 x \in [1, \infty)]$

$\Rightarrow f'(x) > 0, \forall x \in R$

So, $f(x)$ always increases.