Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 595

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\[1)\ 1 + \cos{5x} \bullet \sin{4x} =\]

\[= \cos{4x} \bullet \sin{5x}\]

\[\sin{5x} \bullet \cos{4x} - \sin{4x} \bullet \cos{5x} =\]

\[= 1\]

\[\sin(5x - 4x) = 1\]

\[\sin x = 1\]

\[x = \arcsin 1 + 2\pi n\]

\[x = \frac{\pi}{2} + 2\pi n\]

\[Ответ:\ \ x = \frac{\pi}{2} + 2\pi n.\]

\[2)\ 1 - \sin x \bullet \cos{2x} =\]

\[= \cos x \bullet \sin{2x}\]

\[\sin{2x} \bullet \cos x + \sin x \bullet \cos{2x} = 1\]

\[\sin(2x + x) = 1\]

\[\sin{3x} = 1\]

\[3x = \arcsin 1 + 2\pi n = \frac{\pi}{2} + 2\pi n\]

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

\[x = \frac{\pi}{6} + \frac{2\pi n}{3}\]

\[Ответ:\ \ x = \frac{\pi}{6} + \frac{2\pi n}{3}.\]