$$\eqalign{ {\text{Вычислите:}} \hfill \\ \cos \frac{{2\pi }}{7} + \cos \frac{{4\pi }}{7} + \cos \frac{{6\pi }}{7} \hfill \\ } $$

$$\eqalign{ {\text{Докажите}}{\text{, что}} \hfill \\ \cos \frac{\pi }{{{2^n}}} = \frac{1}{2}\sqrt {2 + \sqrt {2 + \sqrt {2 + ... + \sqrt 2 } } } \hfill \\ (n - 1{\text{ знак корня}}{\text{, }}n \in \mathbb{N}) \hfill \\ } $$

$$\eqalign{ {\text{Вычислите:}} \hfill \\ \cos \frac{\pi }{5} - \cos \frac{{2\pi }}{5}. \hfill \\ } $$

\[{\text{Доказать}}{\text{, что }}\cos \frac{\pi }{5} = \frac{{\sqrt 5 + 1}}{4}.\]

\[\begin{array}{l} {\text{Докажите тождество:}} \hfill \\ {\text{co}}{{\text{s}}^2}\frac{\pi }{7} + {\text{co}}{{\text{s}}^2}\frac{{2\pi }}{7} + {\text{co}}{{\text{s}}^2}\frac{{3\pi }}{7} = \frac{5}{4}. \hfill \\ \end{array}\]

\[\begin{array}{l} {\text{Докажите тождество:}} \hfill \\ {\text{co}}{{\text{s}}^3}\frac{\pi }{7} - {\text{co}}{{\text{s}}^3}\frac{{2\pi }}{7} + {\text{co}}{{\text{s}}^3}\frac{{3\pi }}{7} = \frac{1}{2}. \hfill \\ \end{array}\]