Primitive of Reciprocal of Power of Cosine of a x by Power of Sine of a x/Reduction of Power of Sine

Theorem

 * $\displaystyle \int \frac {\d x} {\sin^m a x \cos^n a x} = \frac {-1} {a \paren {n - 1} \sin^{m - 1} a x \cos^{n - 1} a x} + \frac {m + n - 2} {m - 1} \int \frac {\d x} {\sin^{m - 2} a x \cos^n a x} + C$

Also see

 * Primitive of $\dfrac 1 {\sin^m a x \cos^n a x}$ : Reduction of Power of Cosine