Primitive of Product of Cosecant and Cotangent

Theorem

$\displaystyle \int \csc x \cot x \rd x = -\csc x + C$

where $C$ is an arbitrary constant.

Proof

$\dfrac \d {\d x} \csc x = -\csc x \cot x$

The result follows from the definition of primitive.

$\blacksquare$