Identidades trigonométricas
\[ \cos(a \pm b) = \cos a \cos b \mp \sin a \sin b \qquad \sin(a \pm b) = \sin a \cos b \mp \sin b \cos a \] \[ \cos a \cos b = \frac{1}{2} [ \cos (a-b) + \cos (a+b) ] \qquad \cos^2 a = \frac{1}{2} (1 + \cos 2a) \] \[ \sin a \sin b = \frac{1}{2} [ \cos (a-b) - \cos (a+b) ] \qquad \sin^2 a = \frac{1}{2} (1 - \cos 2a) \] \[ \cos a \sin b = \frac{1}{2} [ \sin (a+b) - \sin (a-b) ] \qquad \cos a \sin a = \frac{1}{2} \sin (2a) \] \[ \ee^{\iu\theta} = \cos \theta + \iu \sin \theta \qquad \cos \theta = \frac{1}{2} (\mathrm{e}^{\iu\theta} + \mathrm{e}^{-\iu\theta}) \qquad \sin \theta = \frac{1}{2\iu} (\mathrm{e}^{\iu\theta} - \mathrm{e}^{-\iu\theta}) \]
Séries
\[ \sum_{k=0}^{\infty} r^k = \frac{1}{1 - r}, \qquad \qquad \sum_{k=0}^{\infty} kr^k = \frac{r}{(1 - r)^2}, \qquad \qquad \sum_{k=0}^{\infty} k^2r^k = \frac{r(1+r)}{(1 - r)^3}. \qquad \qquad (|r| < 1) \]