Вычислить без таблиц: cos п/11 + cos 3п/11 + cos 5п/11 + cos 7п/11 + cos 9п/11

[latex]cos\frac{\pi}{11}+cos\frac{3\pi}{11}+cos\frac{5\pi}{11}+cos\frac{7\pi}{11}+cos\frac{9\pi}{11}=\\\\ \frac{2sin\frac{\pi}{11}(cos\frac{\pi}{11}+cos\frac{3\pi}{11}+cos\frac{5\pi}{11}+cos\frac{7\pi}{11}+cos\frac{9\pi}{11})}{2sin\frac{\pi}{11}}=\\\\ \frac{sin\frac{2\pi}{11}+2sin\frac{\pi}{11}*cos\frac{3\pi}{11}+2sin\frac{\pi}{11}cos\frac{5\pi}{11}+\\\\ 2sin\frac{\pi}{11}*cos\frac{7\pi}{11}+2sin\frac{\pi}{11}*cos\frac{9\pi}{11}}{2sin\frac{\pi}{11}}=\\\\ [/latex] [latex]2sin\frac{\pi}{11}*cos\frac{3\pi}{11}=-sin\frac{2\pi}{11}+sin\frac{4\pi}{11}\\ 2sin\frac{\pi}{11}*cos\frac{5\pi}{11}=-sin\frac{4\pi}{11}+sin\frac{6\pi}{11}\\ 2sin\frac{\pi}{11}*cos\frac{7\pi}{11}=-sin\frac{6\pi}{11}+sin\frac{8\pi}{11}\\ 2sin\frac{\pi}{11}*cos\frac{9\pi}{11}=-sin\frac{8\pi}{11}+sin\frac{10\pi}{11}\\\\ \frac{sin\frac{10\pi}{11}}{2sin\frac{2\pi}{11}}=\frac{1}{2}[/latex]  Ответ [latex] \frac{1}{2}[/latex]