Question

Function $f(x)= \ln \sin x$ is monotonically increasing when-

• A. $x \in(\pi / 2, \pi)$
• B. $x \in(-\pi / 2,0)$
• C. $x \in(0, \pi)$
• D. $x \in(0, \pi / 2)$

Answer 1

Answer: (D)

$f^{\prime}(x)=\cot x$
monotonically increasing $\Rightarrow f^{\prime}(x)>0$
$ \Rightarrow x \in\left(0, \frac{\pi}{2}\right)$