Дано
$$frac{2 sqrt{3} cos{left (105 right )}}{left(-1 + frac{105 cos{left (105 right )}}{sin{left (x right )}}right) sin{left (105 right )}}$$
Подстановка условия
$$frac{2 sqrt{3} cos{left (105 right )}}{left(-1 + frac{105 cos{left (105 right )}}{sin{left (x right )}}right) sin{left (105 right )}}$$
((2*sqrt(3))*cos(105))/(sin(105)*((cos(105)*105)/sin((3)) – 1))
$$frac{2 sqrt{3} cos{left (105 right )}}{left(-1 + frac{105 cos{left (105 right )}}{sin{left ((3) right )}}right) sin{left (105 right )}}$$
((2*sqrt(3))*cos(105))/(sin(105)*((cos(105)*105)/sin(3) – 1))
$$frac{2 sqrt{3} cos{left (105 right )}}{left(frac{105 cos{left (105 right )}}{sin{left (3 right )}} – 1right) sin{left (105 right )}}$$
2*sqrt(3)*cos(105)/((-1 + 105*cos(105)/sin(3))*sin(105))
$$frac{2 sqrt{3} cos{left (105 right )}}{left(frac{105 cos{left (105 right )}}{sin{left (3 right )}} – 1right) sin{left (105 right )}}$$
Численный ответ
-0.834706631641183/(0.970535283537485 + 24.5552222129948/sin(x))
Рациональный знаменатель
$$frac{2 sqrt{3} sin{left (x right )} cos{left (105 right )}}{left(- sin{left (x right )} + 105 cos{left (105 right )}right) sin{left (105 right )}}$$
Объединение рациональных выражений
$$frac{2 sqrt{3} sin{left (x right )} cos{left (105 right )}}{left(- sin{left (x right )} + 105 cos{left (105 right )}right) sin{left (105 right )}}$$
Общее упрощение
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2*/ 3 *sin(x)
——————————
105*sin(105) – sin(x)*tan(105)
$$frac{2 sqrt{3} sin{left (x right )}}{- sin{left (x right )} tan{left (105 right )} + 105 sin{left (105 right )}}$$
Соберем выражение
$$frac{2 sqrt{3} cot{left (105 right )}}{105 cos{left (105 right )} csc{left (x right )} – 1}$$
Общий знаменатель
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2*/ 3 *cos(105)*sin(x)
—————————————-
-sin(105)*sin(x) + 105*cos(105)*sin(105)
$$frac{2 sqrt{3} sin{left (x right )} cos{left (105 right )}}{- sin{left (105 right )} sin{left (x right )} + 105 sin{left (105 right )} cos{left (105 right )}}$$
Тригонометрическая часть
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2*/ 3 *sin(x)
——————————
105*sin(105) – sin(x)*tan(105)
$$frac{2 sqrt{3} sin{left (x right )}}{- sin{left (x right )} tan{left (105 right )} + 105 sin{left (105 right )}}$$
Комбинаторика
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2*/ 3 *cos(105)*sin(x)
———————————
(-sin(x) + 105*cos(105))*sin(105)
$$frac{2 sqrt{3} sin{left (x right )} cos{left (105 right )}}{left(- sin{left (x right )} + 105 cos{left (105 right )}right) sin{left (105 right )}}$$