$$\eqalign{
{\text{Вычислите:}} \hfill \\
\cos \frac{\pi }{5} - \cos \frac{{2\pi }}{5}. \hfill \\
} $$
$$\eqalign{
x = \cos \frac{\pi }{5} - \cos \frac{{2\pi }}{5} \hfill \\
{x^2} = {\left( {\cos \frac{\pi }{5} - \cos \frac{{2\pi }}{5}} \right)^2} = \frac{1}{2}\left( {\cos \frac{{2\pi }}{5} + 1 - \cos \frac{\pi }{5}} \right) \hfill \\
{x^2} = \frac{1}{2}\left( {1 - x} \right) \hfill \\
x = \frac{1}{2} \hfill \\
} $$
\[\frac{1}{2}\]
