Косинус половинного угла

\[\cos{\frac{\alpha}{2}} = \sqrt{\frac{1 + \cos{\alpha}}{2}}\]

\[\sin{\frac{\alpha}{2}} = \sqrt{\frac{1 - \cos{\alpha}}{2}}\]

\[\mathrm{tg}{\frac{\alpha}{2}} = \frac{1 - \cos{\alpha}}{\sin{\alpha}} = \frac{\sin{\alpha}}{1 + \cos{\alpha}}\]

\[\mathrm{ctg}{\frac{\alpha}{2}} = \frac{\sin{\alpha}}{1 - \cos{\alpha}} = \frac{1 + \cos{\alpha}}{\sin{\alpha}}\]