Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1190

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\[1)\ arctg\left( \text{ctg}\frac{5\pi}{6} \right) =\]

\[= \text{arctg}\left( \text{ctg}\left( \frac{\pi}{2} + \frac{\pi}{3} \right) \right) =\]

\[= \text{arctg}\left( - tg\frac{\pi}{3} \right) =\]

\[= - arctg\left( \text{tg}\frac{\pi}{3} \right) = - \frac{\pi}{3}\]

\[2)\ arctg\left( \text{ctg}\frac{3\pi}{4} \right) =\]

\[= \text{arctg}\left( \text{ctg}\left( \frac{\pi}{2} + \frac{\pi}{4} \right) \right) =\]

\[= \text{arctg}\left( - tg\frac{\pi}{4} \right) =\]

\[= - arctg\left( \text{tg}\frac{\pi}{4} \right) = - \frac{\pi}{4}\]

\[3)\ arctg\left( 2\sin\frac{\pi}{3} \right) =\]

\[{= \text{arctg}\left( 2 \bullet \frac{\sqrt{3}}{2} \right) = }{= \text{arctg\ }\sqrt{3} = \frac{\pi}{3}}\]