Power Reduction Formulas

Theorem

 * $\sin^2x = \dfrac {1-\cos2x} 2$


 * $\cos^2x = \dfrac {1+\cos2x} 2$


 * $\tan^2x = \dfrac {1-\cos2x}{1+\cos2x}$

where $\sin, \cos, \tan$ are sine, cosine and tangent.

Comment
The identities for $\sin^2x$ and $\cos^2x$ can be useful for integrating expressions of the form:


 * $\displaystyle \int \sin^mx \ \cos^nx \ \mathrm dx$

where $m$ and $n$ are both even.