Answer
$-\dfrac{1}{2} \cot x +\dfrac{1}{2} \csc x+C$
Work Step by Step
Given: $ \dfrac{1}{2} \int (\csc^2 x ) dx - \dfrac{1}{2} \int (\csc x \cot x) dx$
Thus, $\dfrac{1}{2} \int (\csc^2 x ) dx - \dfrac{1}{2} \int (\csc x \cot x) dx=-\dfrac{1}{2} \cot x +\dfrac{1}{2} \csc x+C$
