If f ( x )= a ( tan x - cot x ), where a >0, then find whether f ( x ) is increasing or decreasing function in its domain.

$$\mathrm{f}^{\prime}(\mathrm{x})=\mathrm{a}\left(\sec ^{2} \mathrm{x}+\operatorname{cosec}^{2} \mathrm{x}\right) $$ As $\displaystyle \mathrm{a}>0$ and $\displaystyle \sec ^{2} \mathrm{x}, \operatorname{cosec}^{2} \mathrm{x}$ are squares, $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})>0$ $\displaystyle \therefore \mathrm{f}(\mathrm{x})$ is an increasing function in its domain.