Answer
$\csc x$
Work Step by Step
Our aim is to solve the function $F(x)=-\ln |\csc x+\cot x|+C$
We differentiate both sides with respect to $x$.
$F^{\prime}(x)=\dfrac{-1}{\csc x+\cot x }\dfrac{d}{dx}[ \csc x+\cot x]+0$
or, $=\dfrac{-1}{\csc x+\cot x }(-\csc x \cot x-\csc^2 x)$
or, $=\dfrac{-\csc x(\cot x+\csc x) }{(\csc x +\cot x)}$
or, $=\csc x$
