Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1025

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\[1)\cos{57{^\circ}30^{'}} \bullet \cos{27{^\circ}30^{'}} +\]

\[+ \sin{57{^\circ}30{^\circ}} \bullet \sin{27{^\circ}30{^\circ}} =\]

\[= \cos\left( 57{^\circ}30^{'} - 27{^\circ}30^{'} \right) =\]

\[= \cos{30{^\circ}} = \frac{\sqrt{3}}{2}\]

\[2)\ \cos{19{^\circ}30^{'}} \bullet \cos{25{^\circ}30^{'}} -\]

\[- \sin{19{^\circ}30{^\circ}} \bullet \sin{25{^\circ}30{^\circ}} =\]

\[= \cos\left( 19{^\circ}30^{'} + 25{^\circ}30^{'} \right) =\]

\[= \cos{45{^\circ}} = \frac{\sqrt{2}}{2}\]

\[3)\cos\frac{7\pi}{9} \bullet \cos\frac{11\pi}{9} - \sin\frac{7\pi}{9} \bullet\]

\[\bullet \sin\frac{11\pi}{9} = \cos\left( \frac{7\pi}{9} + \frac{11\pi}{9} \right) =\]

\[= \cos\frac{18\pi}{9} = \cos{2\pi} = 1\]

\[4)\cos\frac{8\pi}{7} \bullet \cos\frac{\pi}{7} + \sin\frac{8\pi}{7} \bullet \sin\frac{\pi}{7} =\]

\[= \cos\left( \frac{8\pi}{7} - \frac{\pi}{7} \right) = \cos\frac{7\pi}{7} =\]

\[= \cos\pi = - 1\]