formulario goniometria

Addizione e sottrazione

$sin(\alpha +\beta )=sin(\alpha )cos(\beta )+cos(\alpha )sin(\beta )$
$sin(\alpha -\beta )=sin(\alpha )cos(\beta )-sin(\beta )cos(\alpha )$
$cos(\alpha +\beta )=cos(\alpha )cos(\beta )-sin(\alpha )sin(\beta )$
$cos(\alpha -\beta )=cos(\alpha )cos(\beta )+sin(\alpha )sin(\beta )$

$tan(\alpha +\beta )=\frac{tan(\alpha )+tan(\beta )}{1-tan(\alpha )tan(\beta )}$

$tan(\alpha -\beta )=\frac{tan(\alpha )-tan(\beta )}{1+tan(\alpha )tan(\beta )}$

$cot(\alpha +\beta )=\frac{cot(\alpha )cot(\beta )-1}{cot(\alpha )+cot(\beta )}$

$cot(\alpha -\beta )=\frac{cot(\alpha )cot(\beta )+1}{cot(\alpha )-cot(\beta )}$

Duplicazione

$sin(2\alpha )=2sin(\alpha )cos(\alpha )$
$cos(2\alpha )=co{s}^2(\alpha )-si{n}^2(\alpha )$

$tan(2\alpha )=\frac{2tan(\alpha )}{1-ta{n}^2(\alpha )}$

$cot(2\alpha )=\frac{co{t}^2(\alpha )-1}{2co{t}^2(\alpha )}$

Bisezione

$sin(\frac{\alpha }{2})=\pm \sqrt{\frac{1-\cos (\alpha )}{2}}$

$cos(\frac{\alpha }{2})=\pm \sqrt{\frac{1+\cos (\alpha )}{2}}$

$tan(\frac{\alpha }{2})=\pm \sqrt{\frac{1-\cos (\alpha )}{1+\cos (\alpha )}}$

$cot(\frac{\alpha }{2})=\pm \sqrt{\frac{1+\cos (\alpha )}{1-\cos (\alpha )}}$

Prostaferesi

$sin(p)+sin(q)=2sin(\frac{p+q}{2})cos(\frac{p-q}{2})$

$cos(p)+cos(q)=2cos(\frac{p+q}{2})cos(\frac{p-q}{2})$

$sin(p)-sin(q)=2sin(\frac{p-q}{2})cos(\frac{p+q}{2})$

$cos(p)-cos(q)=-2sin(\frac{p+q}{2})sin(\frac{p-q}{2})$

Werner

$sin(\alpha )sin(\beta )=\frac{cos(\alpha -\beta )-cos(\alpha +\beta )}{2}$

$cos(\alpha )cos(\beta )=\frac{cos(\alpha -\beta )+cos(\alpha +\beta )}{2}$

$sin(\alpha )cos(\beta )=\frac{sin(\alpha -\beta )+sin(\alpha +\beta )}{2}$