Answer
$\cot x$
Work Step by Step
Our aim is to solve the function $F(x)=\ln |\sin x|+C$
We differentiate both sides with respect to $x$.
$F^{\prime}(x)=\dfrac{1}{\sin x }\dfrac{d}{dx}[ \sin x]+0$
or, $=\dfrac{1}{\sin x} (\cos x)$
or, $=\cot x$
