\[\begin{array}{l}
{\text{Вычислите:}} \hfill \\
{\text{co}}{{\text{s}}^{10}}\frac{\pi }{{10}} - {\text{co}}{{\text{s}}^{10}}\frac{{3\pi }}{{10}}. \hfill \\
\end{array}\]
\[\begin{array}{l}
{\cos ^2}\frac{\pi }{{10}} = \frac{{1 + \cos \frac{\pi }{5}}}{2} = \frac{{5 + \sqrt 5 }}{8} \hfill \\
{\cos ^2}\frac{{3\pi }}{{10}} = \frac{{1 - \cos \frac{{2\pi }}{5}}}{2} = \frac{{5 - \sqrt 5 }}{8} \hfill \\
\end{array}\]
\[\frac{{275\sqrt 5 }}{{1024}}\]
