ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 1115

\[\boxed{\mathbf{1115}\mathbf{.}}\]

\[\sin\left( x + \frac{\pi}{8} \right)\cos\left( x - \frac{\pi}{24} \right) =\]

\[= \frac{1}{2}\sin\left( 2x + \frac{\pi}{12} \right) + \frac{1}{2}\sin\frac{\pi}{6} =\]

\[= \frac{1}{2}\sin\left( 2x + \frac{\pi}{12} \right) + \frac{1}{4}\]

\[- 1 \leq \sin\left( 2x + \frac{\pi}{12} \right) \leq 1\]

\[- \frac{1}{2} \leq \frac{1}{2}\sin\left( 2x + \frac{\pi}{12} \right) \leq \frac{1}{2}\]

\[- \frac{1}{4} \leq \frac{1}{2}\sin\left( 2x + \frac{\pi}{12} \right) \leq \frac{3}{4}\]

\[\min = - \frac{1}{4};\ \max = \frac{3}{4}.\]