Решебник по геометрии 9 класс Мерзляк Задание 17

\[1)\ \frac{\sin{18{^\circ}}}{\sin{162{^\circ}}} = \frac{\sin{18{^\circ}}}{\sin(180{^\circ} - 18{^\circ})} =\]

\[= \frac{\sin{18{^\circ}}}{\sin{18{^\circ}}} = 1;\]

\[2)\ \frac{\cos{18{^\circ}}}{\cos{162{^\circ}}} = \frac{\cos{18{^\circ}}}{\cos(180{^\circ} - 18{^\circ})} =\]

\[= \frac{\cos{18{^\circ}}}{- \cos{18{^\circ}}} = - 1;\]

\[3)\ \frac{tg\ 18{^\circ}}{tg\ 162{^\circ}} = \frac{tg\ 18{^\circ}}{\text{tg}(180{^\circ} - 18{^\circ})} =\]

\[= \frac{tg\ 18{^\circ}}{- tg\ 18{^\circ}} = - 1;\]

\[4)\ \frac{ctg\ 18{^\circ}}{ctg\ 162{^\circ}} = \frac{ctg\ 18{^\circ}}{\text{ctg}(180{^\circ} - 18{^\circ})} =\]

\[= \frac{ctg\ 18{^\circ}}{- ctg\ 18{^\circ}} = - 1.\]