\[\begin{array}{l} {\text{Докажите тождества:}} \hfill \\ {\text{а) }}\prod\limits_{k = 1}^n {\sin \frac{{\pi k}}{{2n + 1}}} = \frac{{\sqrt {2n + 1} }}{{{2^n}}}; \hfill \\ {\text{б) }}\prod\limits_{k = 1}^{n - 1} {\sin \frac{{\pi k}}{{2n}}} = \frac{{\sqrt n }}{{{2^{n - 1}}}}; \hfill \\ {\text{в) }}\prod\limits_{k = 1}^n {\cos \frac{{\pi k}}{{2n + 1}}} = \frac{1}{{{2^n}}}; \hfill \\ {\text{г) }}\prod\limits_{k = 1}^{n - 1} {\cos \frac{{\pi k}}{{2n}}} = \frac{{\sqrt n }}{{{2^{n - 1}}}}. \hfill \\ \end{array}\]