$$\begin{array}{l} {\text{Пусть }}n \in \mathbb{N}.{\text{ Докажите формулу:}} \hfill \\ \operatorname{tg} \left( {n\operatorname{arctg} x} \right) = \frac{{\frac{1}{{2i}}\left( {{{\left( {1 + x \cdot i} \right)}^n} - {{\left( {1 - x \cdot i} \right)}^n}} \right)}}{{\frac{1}{2}\left( {{{\left( {1 + x \cdot i} \right)}^n} + {{\left( {1 - x \cdot i} \right)}^n}} \right)}}. \hfill \\ \end{array}$$