Решебник по геометрии 9 класс Мерзляк Задание 16

\[1)\ 2\sin{150{^\circ}} - 4\cos{120{^\circ}} =\]

\[= 2\sin{30{^\circ}} + 4\cos{60{^\circ}} =\]

\[= 2 \bullet \frac{1}{2} + 4 \bullet \frac{1}{2} = 1 + 2 = 3.\]

\[2)\ tg\ 45{^\circ}\sin{120{^\circ}}ctg\ 150{^\circ} =\]

\[= 1 \bullet \sin{60{^\circ}} \bullet ( - ctg\ 30{^\circ}) =\]

\[= \frac{\sqrt{3}}{2} \bullet \left( - \sqrt{3} \right) = - \frac{3}{2} = - 1,5.\]

\[= \left( \frac{\sqrt{3}}{3} \bullet \frac{\sqrt{2}}{2} - \sqrt{3} \bullet \frac{\sqrt{2}}{2} \right)^{2} =\]

\[= \left( \frac{\sqrt{6} - 3\sqrt{6}}{6} \right)^{2} = \left( - \frac{2\sqrt{6}}{6} \right)^{2} =\]

\[= \left( - \frac{2}{\sqrt{6}} \right)^{2} = \frac{4}{6} = \frac{2}{3}.\]