Question

State whether f(x) = tan x − x is increasing or decreasing its domain.

Answer 1

$$\begin{gathered} f\left(x\right)=\tan x-x \\ f\text{'}\left(x\right)={\sec }^{2}x-1 \\ ={\tan }^{2}x⩾0,\forall x\in \left[0,2\mathrm{\pi }\right] \\ \text{So,}\mathit{\text{f}}\text{(}\mathit{\text{x}})\text{is increasing in its domain.} \end{gathered}$$