Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 954

\[\left\{ \begin{matrix} \cos\left( \frac{\pi}{2} + x \right) + \sin\left( \frac{3}{2}\pi - y \right) = 1 \\ x + y = - \frac{3\pi}{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[1)\ \cos\left( \frac{\pi}{2} + x \right) + \sin\left( \frac{3}{2}\pi - y \right) = 1\]

\[y = - x - \frac{3\pi}{2}.\]

\[2)\ x + y = - \frac{3\pi}{2}\]

\[\cos\left( \frac{\pi}{2} + x \right) + \sin\left( \frac{3\pi}{2} + x + \frac{3\pi}{2} \right) = 1\]

\[\cos\left( \frac{\pi}{2} + x \right) + \sin(3\pi + x) = 1\]

\[- \sin x - \sin x = 1\]

\[2\sin x = - 1\]

\[\sin x = - \frac{1}{2}\]

\[x = ( - 1)^{n + 1} \bullet \arcsin\frac{1}{2} + \pi n =\]

\[= ( - 1)^{n + 1} \bullet \frac{\pi}{6} + \pi n;\]

\[y = - \frac{3\pi}{2} + ( - 1)^{n} \bullet \frac{\pi}{6} - \pi n.\]

\[Ответ:\ \ \]

\[\left( ( - 1)^{n + 1}\frac{\pi}{6} + \pi n;\ - \frac{3\pi}{2} + ( - 1)^{n}\frac{\pi}{6} - \pi n \right).\]