Дано
$$- x sin{left (60 right )} + – x left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – frac{625}{2}$$
Подстановка условия
$$- x sin{left (60 right )} + – x left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – frac{625}{2}$$
-625/2 – (-1/3)*(cos(30) – 150/cos(30))*cos(60) – (-1/3)*sin(60)
$$- (-1/3) sin{left (60 right )} + – (-1/3) left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – frac{625}{2}$$
-625/2 – (-(cos(30) – 150/cos(30))/3)*cos(60) – (-1)*sin(60)/3
$$- frac{625}{2} – – frac{1}{3} left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – – frac{1}{3} sin{left (60 right )}$$
-625/2 + sin(60)/3 – (50/cos(30) – cos(30)/3)*cos(60)
$$- frac{625}{2} + frac{1}{3} sin{left (60 right )} – left(- frac{1}{3} cos{left (30 right )} + frac{50}{cos{left (30 right )}}right) cos{left (60 right )}$$
Степени
$$- x left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – x sin{left (60 right )} – frac{625}{2}$$
Численный ответ
-312.5 – 925.711028573903*x
Рациональный знаменатель
$$frac{1}{2 cos{left (30 right )}} left(- 2 x left(-150 + cos^{2}{left (30 right )}right) cos{left (60 right )} – 2 x sin{left (60 right )} cos{left (30 right )} – 625 cos{left (30 right )}right)$$
Объединение рациональных выражений
$$frac{1}{2 cos{left (30 right )}} left(- 2 x left(-150 + cos^{2}{left (30 right )}right) cos{left (60 right )} – 2 x sin{left (60 right )} cos{left (30 right )} – 625 cos{left (30 right )}right)$$
Общее упрощение
(625 + 2*x*sin(60))*cos(30) / 2
– ————————— + x*149 + sin (30)/*cos(60)
2
———————————————————-
cos(30)
$$frac{1}{cos{left (30 right )}} left(x left(sin^{2}{left (30 right )} + 149right) cos{left (60 right )} – frac{1}{2} left(2 x sin{left (60 right )} + 625right) cos{left (30 right )}right)$$
Соберем выражение
$$- x sin{left (60 right )} – x left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – frac{625}{2}$$
625 x*cos(30) x*cos(90)
– — – x*sin(60) – ——— – ——— + 150*x*cos(60)*sec(30)
2 2 2
$$150 x cos{left (60 right )} sec{left (30 right )} – frac{x}{2} cos{left (30 right )} – frac{x}{2} cos{left (90 right )} – x sin{left (60 right )} – frac{625}{2}$$
Общий знаменатель
625 150*x*cos(60)
– — – x*sin(60) – x*cos(30)*cos(60) + ————-
2 cos(30)
$$frac{150 x cos{left (60 right )}}{cos{left (30 right )}} – x cos{left (30 right )} cos{left (60 right )} – x sin{left (60 right )} – frac{625}{2}$$
Тригонометрическая часть
625 / 150
– — – x*sin(60) – x*|- ——- + cos(30)|*cos(60)
2 cos(30) /
$$- x left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – x sin{left (60 right )} – frac{625}{2}$$
Комбинаторика
/ 2
-625*cos(30) – 300*x*cos(60) + 2*x*cos (30)*cos(60) + 2*x*cos(30)*sin(60)/
—————————————————————————-
2*cos(30)
$$- frac{1}{2 cos{left (30 right )}} left(2 x sin{left (60 right )} cos{left (30 right )} + 2 x cos^{2}{left (30 right )} cos{left (60 right )} – 300 x cos{left (60 right )} + 625 cos{left (30 right )}right)$$
Раскрыть выражение
625 / 150
– — – x*sin(60) – x*|- ——- + cos(30)|*cos(60)
2 cos(30) /
$$- x left(- frac{150}{cos{left (30 right )}} + cos{left (30 right )}right) cos{left (60 right )} – x sin{left (60 right )} – frac{625}{2}$$
