Show that f(x)= is an increasing function on (- 2 , 2 ). - Vidyadip

Question

Show that $\text{f}(\text{x})=\tan\text{x}$ is an increasing function on $\Big(\frac{-\pi}{2},\frac{\pi}{2}\Big).$

✓

Answer

We have,
$\text{f}(\text{x})=\tan\text{x}$
$\therefore\ \text{f}'(\text{x})=\sec^2\text{x}$
Now,
$\text{x}\in\Big(\frac{-\pi}{2}\frac{\pi}{2}\Big)$
$\Rightarrow\sec^2\text{x}>0$
$\Rightarrow\text{f}'(\text{x})>0$
Hence, f(x) is increasing function on $\Big(\frac{-\pi}{2},\frac{\pi}{2}\Big).$

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