# Prospetto di formule trigonometriche notevoli

Somma Sottrazione Duplicazione Bisezione
Sen sen(α+β) sen(α-β) sen(2α) sen(α/2)
senα·cosβ+senβ·cosα senα·cosβ-senβ·cosα 2senα·cosα $±\sqrt{\frac{1-\mathrm{cos\alpha }}{2}}$
Cos cos(α+β) cos(α-β) cos(2α) cos(α/2)
cosα·cosβ-senα·senβ cosα·cosβ+senα·senβ cos2α-sen2α $±\sqrt{\frac{1+\mathrm{cos\alpha }}{2}}$
Tg tg(α+β) tg(α-β) tg(2α) tg(α/2)
$\frac{\mathrm{tg\alpha }+\mathrm{tg\beta }}{1-\mathrm{tg\alpha }·\mathrm{tg\beta }}$ $\frac{\mathrm{tg\alpha }-\mathrm{tg\beta }}{1+\mathrm{tg\alpha }·\mathrm{tg\beta }}$ $\frac{\mathrm{tg\alpha }}{1-{\mathrm{tg\alpha }}^{2}}$ $±\sqrt{\frac{1-\mathrm{cos\alpha }}{1+\mathrm{cos\alpha }}}$
Prostaferesi
sen(α)+sen(β) $2\frac{\mathrm{sen}\left(\alpha +\beta \right)}{2}·\frac{\mathrm{cos}\left(\alpha -\beta \right)}{2}$
sen(α)-sen(β) $2\frac{\mathrm{sen}\left(\alpha -\beta \right)}{2}·\frac{\mathrm{cos}\left(\alpha +\beta \right)}{2}$
cos(α)+cos(β) $2\frac{\mathrm{cos}\left(\alpha +\beta \right)}{2}·\frac{\mathrm{cos}\left(\alpha -\beta \right)}{2}$
cos(α)-cos(β) $-2\frac{\mathrm{sen}\left(\alpha +\beta \right)}{2}·\frac{\mathrm{sen}\left(\alpha -\beta \right)}{2}$
Werner
sen(α)cos(β) $\frac{\mathrm{sen}\left(\alpha +\beta \right)+\mathrm{sen}\left(\alpha -\beta \right)}{2}$
sen(α)sen(β) $\frac{\mathrm{cos}\left(\alpha -\beta \right)-\mathrm{cos}\left(\alpha +\beta \right)}{2}$
cos(α)cos(β) $\frac{\mathrm{cos}\left(\alpha +\beta \right)+\mathrm{cos}\left(\alpha -\beta \right)}{2}$
Parametriche
sen(α) $\frac{2\mathrm{tan}\left(\frac{\alpha }{2}\right)}{1+{\mathrm{tan}}^{2}\left(\frac{\alpha }{2}\right)}$
cos(α) $\frac{1-{\mathrm{tan}}^{2}\left(\frac{\alpha }{2}\right)}{1+{\mathrm{tan}}^{2}\left(\frac{\alpha }{2}\right)}$