Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 544

\[\boxed{\mathbf{544}\mathbf{.}}\]

\[\mathbf{Тождество:}\]

\[tg\ a + tg\ \beta = \frac{\sin a}{\cos a} + \frac{\sin\beta}{\cos\beta} =\]

\[= \frac{\sin a \bullet \cos\beta + \sin\beta \bullet \cos\alpha}{\cos a \bullet \cos\beta} =\]

\[= \frac{\sin(a + \beta)}{\cos a \bullet \cos\beta}\]

\[Что\ и\ требовалось\ доказать.\]

\[1)\ tg\ 267{^\circ} + tg\ 93{^\circ} =\]

\[= \frac{\sin(267{^\circ} + 93{^\circ})}{\cos{267{^\circ}} \bullet \cos{93{^\circ}}} =\]

\[= \frac{\sin{360{^\circ}}}{\cos{267{^\circ}} \bullet \cos{93{^\circ}}} = 0\ \]

\[2)\ tg\frac{5\pi}{12} + tg\frac{7\pi}{12} =\]

\[= \frac{\sin\left( \frac{5\pi}{12} + \frac{7\pi}{12} \right)}{\cos\frac{5\pi}{12} \bullet \cos\frac{7\pi}{12}} =\]

\[= \frac{\sin\pi}{\cos\frac{5\pi}{12} \bullet \cos\frac{7\pi}{12}} = 0\]