Formulaire de trigonométrie

Formules d'addition

$\cos(\alpha+\beta)=\cos \alpha.\cos \beta - \sin \alpha.\sin \beta$
$\cos(\alpha-\beta)=\cos \alpha.\cos \beta + \sin \alpha.\sin \beta$
$\sin(\alpha+\beta)=\sin \alpha.\cos \beta + \sin \beta.\cos \alpha$
$\sin(\alpha-\beta)=\sin \alpha.\cos \beta - \sin \beta.\cos \alpha$
$\tan (\alpha+\beta)=\dfrac{\tan \alpha + \tan \beta}{1-\tan \alpha.\tan \beta}$
$\tan (\alpha-\beta)=\dfrac{\tan \alpha - \tan \beta}{1+\tan \alpha.\tan \beta}$

Formules de duplication

$\cos \left(2\alpha\right) = \cos^2 \alpha-\sin^2 \alpha$
- $\cos \left(2\alpha\right) = 2.\cos^2 \alpha-1$
- $\cos \left(2\alpha\right) = 1-2.\sin^2 \alpha$
$\sin \left(2\alpha\right) = 2.\sin \alpha.\cos \alpha$
$\tan \left(2\alpha\right) = \dfrac{2\tan \alpha}{1-\tan^2 \alpha}$

Formules de Carnot

Formules de Simpson (somme → produit)

$\cos \alpha + \cos \beta = 2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$
$\sin \alpha + \sin \beta = 2\sin\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$
$\cos \alpha - \cos \beta = -2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)$
$\sin \alpha - \sin \beta = 2\cos\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)$
$\tan \alpha + \tan \beta = \dfrac{\sin\left(\alpha+\beta\right)}{\cos \alpha \cos \beta}$
$\tan \alpha - \tan \beta = \dfrac{\sin\left(\alpha-\beta\right)}{\cos \alpha \cos \beta}$

Formules de linéarisation (produit → somme)

$\cos \alpha\cdot\cos \beta=\dfrac{{\cos{\left(\alpha+\beta\right)}+\cos{\left(\alpha-\beta\right)}}}{2}$
$\sin \alpha\cdot\cos \beta=\dfrac{{\sin{\left(\alpha+\beta\right)}+\sin{\left(\alpha-\beta\right)}}}{2}$
$\sin \alpha\cdot\sin \beta=\dfrac{{\cos{\left(\alpha-\beta\right)}-\cos{\left(\alpha+\beta\right)}}}{2}$
$\cos \alpha\cdot\sin \beta=\dfrac{{\sin{\left(\alpha+\beta\right)}-\sin{\left(\alpha-\beta\right)}}}{2}$

Formules de demi-angle