Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 543

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\[= 4\cos{1{^\circ}} \bullet \cos{2{^\circ}} \bullet \cos{25{^\circ}}\]

\[2)\cos\frac{\pi}{12} + \cos\frac{\pi}{4} + \cos\frac{5\pi}{6} =\]

\[= 2 \bullet \cos\frac{\pi}{6} \bullet \cos\frac{\pi}{12} - \cos\frac{\pi}{6} =\]

\[= 2\cos\frac{\pi}{6} \bullet \left( \cos\frac{\pi}{12} - \frac{1}{2} \right) =\]

\[= 2 \bullet \frac{\sqrt{3}}{2} \bullet \left( \cos\frac{\pi}{12} - \cos\frac{\pi}{3} \right) =\]

\[= - 2\sqrt{3} \bullet \sin\frac{5\pi}{24} \bullet \sin\left( - \frac{3\pi}{24} \right) =\]

\[= 2\sqrt{3} \bullet \sin\frac{5\pi}{24} \bullet \sin\frac{\pi}{8}\]