The function $f(x)=tan x -x $ for $ x\in \left(0, \frac{\pi}{2}\right)$ is :

increase function decreasing function neither increasing nor decreasing function strictly decreasing function

increase function

The correct answer is Option (1) → increase function $f(x)=tan x -x $ so $f'(x)=\sec x-1$ for $ x\in \left(0, \frac{\pi}{2}\right)$ $\sec x>1$ so $f'(x)>0$ $f(x)$ → increasing