Косинус двойного угла

\[\cos{2 \alpha} = \cos^2{\alpha} - \sin^2{\alpha}\]

\[\sin{2 \alpha} = 2 \sin{\alpha} \cos{\alpha}\]

\[\mathrm{tg}{2 \alpha} = \frac{2 \mathrm{tg}{\alpha}}{1 - \mathrm{tg^2}{\alpha}}\]

\[\mathrm{ctg}{2 \alpha} = \frac{\mathrm{ctg^2}{\alpha} - 1}{2 \mathrm{ctg}{\alpha}} = \frac{\mathrm{ctg}{\alpha} - \mathrm{tg}{\alpha}}{2}\]