# Primitive of Reciprocal of Cosecant of a x

## Theorem

$\displaystyle \int \frac {\d x} {\csc a x} = \frac {-\cos a x} a + C$

## Proof

 $\displaystyle \int \frac {\d x} {\csc a x}$ $=$ $\displaystyle \int \sin a x \rd x$ Cosecant is Reciprocal of Sine $\displaystyle$ $=$ $\displaystyle \frac {-\cos a x} a + C$ Primitive of $\sin a x$

$\blacksquare$