Primitive of Power of Cosine of a x over Power of Sine of a x/Reduction of Both Powers

Theorem

 * $\displaystyle \int \frac {\cos^m a x} {\sin^n a x} \ \mathrm d x = \frac {-\cos^{m - 1} a x} {a \left({n - 1}\right) \sin^{n - 1} a x} - \frac {m - 1} {n - 1} \int \frac {\cos^{m - 2} a x} {\sin^{n - 2} a x} \ \mathrm d x$