Power Reduction Formulas

Fifth Power of Cosine
where $\sin, \cos$ and $\tan$ denote sine, cosine and tangent respectively.

Fourth Power of Hyperbolic Cosine
where $\sinh$ and $\cosh$ denote hyperbolic sine and hyperbolic cosine respectively.

Comment
The identities for $\sin^m x$ and $\cos^n x$ can be useful for integrating expressions of the form:


 * $\displaystyle \int \sin^m x \ \cos^n x \ \mathrm d x$