$\mathrm{F}(\mathrm{x})=\log |\sin \mathrm{x}|$, where $\mathrm{x} \in(0, \pi)$ is strictly increasing on
$\mathrm{F}(\mathrm{x})=\log |\sin \mathrm{x}|$, where $\mathrm{x} \in(0, \pi)$ is strictly increasing on
$\left(\frac{\pi}{2}, \pi\right)$ only
$(0, \pi)$ only
$\left(0, \frac{\pi}{2}\right)$ only
$\left(\frac{\pi}{4}, \frac{3 \pi}{4}\right)$ only
Solution
$f(x)=\log |\sin x|$, where $x \in(0, \pi)$
$\therefore \mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{\sin \mathrm{x}} \times \cos \mathrm{x}=\cot \mathrm{x}$
When $\mathrm{f}^{\prime}(\mathrm{x})>0$, we say $\frac{\cos \mathrm{x}}{\sin \mathrm{x}}>0$
Here $\sin x>0 \ldots[x \in(0, \pi)]$
for the function to be strictly increasing, $\cos x>0$
$\rightarrow \mathrm{x} \in\left(0, \frac{\pi}{2}\right)$ only.