\[\begin{array}{l}
{\text{Решите уравнение:}} \hfill \\
\operatorname{arctg} x = \arcsin \frac{1}{x}. \hfill \\
\end{array}\]
\[\operatorname{arctg} x = \arcsin \frac{1}{x} \Leftrightarrow \frac{1}{{x\sqrt {1 - \frac{1}{{{x^2}}}} }} = x \Leftrightarrow x = \pm \frac{{\sqrt {2\sqrt 5 + 2} }}{2}\]
\[x = \pm \frac{{\sqrt {2\sqrt 5 + 2} }}{2}\]
