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