ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 1028

\[\boxed{\mathbf{1028.}}\]

\[1)\sin{73{^\circ}} \bullet \cos{17{^\circ}} +\]

\[+ \cos{73{^\circ}} \bullet \sin{17{^\circ}} =\]

\[= \sin(73{^\circ} + 17{^\circ}) = \sin{90{^\circ}} = 1\]

\[2)\sin{73{^\circ}} \bullet \cos{13{^\circ}} - \cos{73{^\circ}} \bullet\]

\[\bullet \sin{13{^\circ}} = \sin(73{^\circ} - 13{^\circ}) =\]

\[= \sin{60{^\circ}} = \frac{\sqrt{3}}{2}\]

\[3)\sin\frac{5\pi}{12} \bullet \cos\frac{\pi}{12} + \sin\frac{\pi}{12} \bullet\]

\[\bullet \cos\frac{5\pi}{12} = \sin\left( \frac{5\pi}{12} + \frac{\pi}{12} \right) =\]

\[= \sin\frac{6\pi}{12} = \sin\frac{\pi}{2} = 1\]

\[4)\sin\frac{7\pi}{12} \bullet \cos\frac{\pi}{12} - \sin\frac{\pi}{12} \bullet\]

\[\bullet \cos\frac{7\pi}{12} = \sin\left( \frac{7\pi}{12} - \frac{\pi}{12} \right) =\]

\[= \sin\frac{6\pi}{12} = \sin\frac{\pi}{2} = 1\]