Решебник по геометрии 9 класс Мерзляк Задание 15

\[1)\ 2\sin{120{^\circ}} + 4\cos{150{^\circ}} - 2\ tg\ 135{^\circ} =\]

\[= 2\sin{60{^\circ}} - 4\cos{30{^\circ}} + 2\ tg\ 45{^\circ} =\]

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

\[= - \frac{1}{2} - 8 \bullet \left( \frac{1}{2} \right)^{2} + 0 =\]

\[= - \frac{1}{2} - 2 = - 2\frac{1}{2}.\]

\[= - 1 \bullet \left( \sin{45{^\circ}} \bullet \sqrt{3} + \cos{45{^\circ}} \right)^{2} =\]

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

\[= - \left( \frac{\sqrt{3} + 1}{\sqrt{2}} \right)^{2} = - \frac{3 + 2\sqrt{3} + 1}{2} =\]

\[= - \frac{4 + 2\sqrt{3}}{2} = - 2 - \sqrt{3}.\]

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