Is function 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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