Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 758

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\[1)\ y = \sin x + \cos x;\]

\[Ответ:\ \ x \in R.\]

\[2)\ y = \sin x + tg\ x;\]

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

\[3)\ y = \sqrt{\sin x};\]

\[\sin x \geq 0\]

\[\arcsin 0 + 2\pi n \leq x \leq \pi - \arcsin 0 + 2\pi n.\]

\[Ответ:\ \ 2\pi n \leq x \leq \pi + 2\pi n.\]

\[4)\ y = \sqrt{\cos x};\]

\[\cos x \geq 0\]

\[- \arccos 0 + 2\pi n \leq x \leq \arccos 0 + 2\pi n.\]

\[Ответ:\ \]

\[- \frac{\pi}{2} + 2\pi n \leq x \leq \frac{\pi}{2} + 2\pi n.\]

\[5)\ y = \frac{2x}{2\sin x - 1};\]

\[2\sin x - 1 \neq 0\]

\[2\sin x \neq 1\]

\[\sin x \neq \frac{1}{2}\]

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

\[x \neq ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n.\]

\[Ответ:\ \ x \neq ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n.\]

\[6)\ y = \frac{\cos x}{2\sin^{2}x - \sin x};\]

\[2\sin^{2}x - \sin x \neq 0\]

\[\sin x \bullet \left( 2\sin x - 1 \right) \neq 0\]

\[\sin x \neq 0;\]

\[x \neq \arcsin 0 + \pi n = \pi n.\]

\[2\sin x - 1 \neq 0\]

\[2\sin x \neq 1\]

\[\sin x \neq \frac{1}{2}\]

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

\[x \neq ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n.\]

\[Ответ:\ \ x \neq \pi n;\ \ \]

\[x \neq ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n.\]