Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 615

\[\boxed{\mathbf{615}\mathbf{.}}\]

\[{\text{arc}\text{tg}}a = x,\ если\text{tg}x = a\ \ и\ \]

\[- \frac{\pi}{2} < x < \frac{\pi}{2}.\]

\[a - положительное\ число:\]

\[\text{tg}\left( \text{arctg}a \right) = \text{tg}x = a;\]

\[\text{tg}\left( \text{arctg}( - a) \right) =\]

\[= \text{tg}\left( - \text{arctg}(a) \right) = \text{tg}( - x) =\]

\[= - \text{tg}x = - a.\]

\[1)\ tg(arctg\ 2,1) = 2,1\]

\[2)\ tg\left( \text{arctg}( - 0,3) \right) = - 0,3\]

\[3)\ tg(\pi - arctg\ 7) =\]

\[= \text{tg}( - arctg\ 7) =\]

\[= - tg(arctg\ 7) = - 7\]

\[4)\ ctg\left( \frac{\pi}{2} + arctg\ 6 \right) =\]

\[= - tg(arctg\ 6) = - 6\]