\[\begin{array}{l} \sin 2x = \frac{{2\operatorname{tg} x}}{{1 + {{\operatorname{tg} }^2}x}} \hfill \\ \cos 2x = \frac{{1 - {{\operatorname{tg} }^2}x}}{{1 + {{\operatorname{tg} }^2}x}} \hfill \\ \end{array}\]