Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 775

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\[1)\sin x \geq \cos x\]

\[\sin x - \cos x \geq 0\]

\[\sqrt{2} \bullet \left( \sin x \bullet \frac{1}{\sqrt{2}} - \cos x \bullet \frac{1}{\sqrt{2}} \right) \geq 0\]

\[\sin x \bullet \cos\frac{\pi}{4} - \cos x \bullet \sin\frac{\pi}{4} \geq 0\]

\[\sin\left( x - \frac{\pi}{4} \right) \geq 0\]

\[\arcsin 0 + 2\pi n \leq x - \frac{\pi}{4} \leq \pi - \arcsin 0 + 2\pi n\]

\[2\pi n \leq x - \frac{\pi}{4} \leq \pi + 2\pi n\]

\[Ответ:\ \ \]

\[\frac{\pi}{4} + 2\pi n \leq x \leq \frac{5\pi}{4} + 2\pi n.\]

\[2)\ tg\ x > \sin x\]

\[tg\ x - \sin x > 0\]

\[\frac{\sin x}{\cos x} - \sin x > 0\]

\[\frac{\sin x - \sin x \bullet \cos x}{\cos x} > 0\]

\[\frac{\sin x \bullet \left( 1 - \cos x \right)}{\cos x} > 0\]

\[tg\ x \bullet \left( 1 - \cos x \right) > 0\]

\[1)\ 1 - \cos x > 0\]

\[- \cos x > - 1\]

\[\cos x < 1\]

\[\cos x \neq 0\]

\[x \neq \arccos 0 + \pi n = \frac{\pi}{2} + \pi n.\]

\[2)\ tg\ x > 0\]

\[arctg\ 0 + \pi n < x < \frac{\pi}{2} + \pi n\]

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