Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1027

\[\boxed{\mathbf{1027.}}\]

\[1)\cos{3a} \bullet \cos a - \sin a \bullet \sin{3a} =\]

\[= \cos(3a + a) = \cos{4a}\]

\[2)\cos{5\beta} \bullet \cos{2\beta} +\]

\[+ \sin{5\beta} \bullet \sin{2\beta} =\]

\[= \cos(5\beta - 2\beta) = \cos{3\beta}\]

\[3)\cos\left( \frac{\pi}{7} + a \right) \bullet \cos\left( \frac{5\pi}{14} - a \right) -\]

\[- \sin\left( \frac{\pi}{7} + a \right) \bullet \sin\left( \frac{5\pi}{14} - a \right) =\]

\[= \cos\left( \frac{\pi}{7} + a + \frac{5\pi}{14} - a \right) =\]

\[= \cos\left( \frac{2\pi}{14} + \frac{5\pi}{14} \right) = \cos\frac{7\pi}{14} =\]

\[= \cos\frac{\pi}{2} = 0\]

\[4)\cos\left( \frac{7\pi}{5} + a \right) \bullet \cos\left( \frac{2\pi}{5} + a \right) +\]

\[+ \sin\left( \frac{7\pi}{5} + a \right) \bullet \sin\left( \frac{2\pi}{5} + a \right) =\]

\[= \cos\left( \frac{7\pi}{5} + a - \frac{2\pi}{5} - a \right) =\]

\[= \cos\frac{5\pi}{5} = \cos\pi = - 1\]