Формулы двойного аргумента (угла)

$$sin2x=2cosxsinx$$

\begin{align} sin2x &=\frac{2tgx}{1+tg^2x}\\ &= \frac{2ctgx}{1+ctg^2x}\\ &= \frac{2}{tgx+ctgx} \end{align}

\begin{align} cos2x & = \cos^2x-sin^2x\\ &= 2cos^2x-1\\ &= 1-2sin^2x \end{align}

\begin{align} cos2x & = \frac{1-tg^2x}{1+tg^2x}\\ &= \frac{ctg^2x-1}{ctg^2x+1}\\ &= \frac{ctgx-tgx}{ctgx+tgx} \end{align}

\begin{align} tg2x & = \frac{2tgx}{1-tg^2x}\\ &= \frac{2ctgx}{ctg^2x-1}\\ &= \frac{2}{ctgx-tgx} \end{align}

\begin{align} ctg2x & = \frac{ctg^2x-1}{2ctgx}\\ &= \frac{2ctgx}{ctg^2x-1}\\ &= \frac{ctgx-tgx}{2} \end{align}