Is function tan x decreasing on (0, 2 )? - Vidyadip

Question

Is function tan x decreasing on ($0, \frac{\pi}{2}$)?

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Answer

Let $f_3 = tan\ x$
$\therefore \mathrm{f}_{3}^{\prime}(\mathrm{x})=\sec ^{2} \mathrm{x}$
In interval $\left(0, \frac{\pi}{2}\right)$
$\mathrm{f}_{3}^{\prime}(\mathrm{x})=\sec ^{2} \mathrm{x}>0$
Therefore, $f_3$ is strictly increasing in interval $\left(0, \frac{\pi}{2}\right)$.

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