Дано
$$frac{4 sin{left (frac{19 p}{12} right )} + 4 cos{left (frac{25 p}{12} right )}}{- 4 cos{left (frac{p}{12} right )} – 2 cos{left (frac{11 p}{12} right )}}$$
Подстановка условия
$$frac{4 sin{left (frac{19 p}{12} right )} + 4 cos{left (frac{25 p}{12} right )}}{- 4 cos{left (frac{p}{12} right )} – 2 cos{left (frac{11 p}{12} right )}}$$
(4*cos((25*(-3))/12) + 4*sin((19*(-3))/12))/(-4*cos((-3)/12) – 2*cos((11*(-3))/12))
$$frac{4 sin{left (frac{19 (-3)}{12} right )} + 4 cos{left (frac{25 (-3)}{12} right )}}{- 4 cos{left (frac{(-3)}{12} right )} – 2 cos{left (frac{11 (-3)}{12} right )}}$$
(4*cos((25*(-3))/12) + 4*sin((19*(-3))/12))/(-4*cos(-1/4) – 2*cos((11*(-3))/12))
$$frac{4 sin{left (frac{-57}{12} 1 right )} + 4 cos{left (frac{-75}{12} 1 right )}}{- 4 cos{left (- frac{1}{4} right )} – 2 cos{left (frac{-33}{12} 1 right )}}$$
(-4*sin(19/4) + 4*cos(25/4))/(-4*cos(1/4) – 2*cos(11/4))
$$frac{- 4 sin{left (frac{19}{4} right )} + 4 cos{left (frac{25}{4} right )}}{- 4 cos{left (frac{1}{4} right )} – 2 cos{left (frac{11}{4} right )}}$$
Численный ответ
(4.0*cos((25*p)/12) + 4.0*sin((19*p)/12))/(-2.0*cos((11*p)/12) – 4.0*cos(p/12))
Рациональный знаменатель
$$frac{- 2 sin{left (frac{19 p}{12} right )} – 2 cos{left (frac{25 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}}$$
Объединение рациональных выражений
$$frac{2 sin{left (frac{19 p}{12} right )} + 2 cos{left (frac{25 p}{12} right )}}{- 2 cos{left (frac{p}{12} right )} – cos{left (frac{11 p}{12} right )}}$$
Общее упрощение
/ /25*p /19*p
-|2*cos|—-| + 2*sin|—-||
12 / 12 //
—————————–
/p /11*p
2*cos|–| + cos|—-|
12/ 12 /
$$- frac{2 sin{left (frac{19 p}{12} right )} + 2 cos{left (frac{25 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}}$$
Соберем выражение
$$- frac{2 sin{left (frac{19 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}} – frac{2 cos{left (frac{25 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}}$$
Общий знаменатель
/ /25*p /19*p
-|2*cos|—-| + 2*sin|—-||
12 / 12 //
—————————–
/p /11*p
2*cos|–| + cos|—-|
12/ 12 /
$$- frac{2 sin{left (frac{19 p}{12} right )} + 2 cos{left (frac{25 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}}$$
Тригонометрическая часть
/ /25*p /19*p
-2*|cos|—-| + sin|—-||
12 / 12 //
————————–
/p /11*p
2*cos|–| + cos|—-|
12/ 12 /
$$- frac{2 sin{left (frac{19 p}{12} right )} + 2 cos{left (frac{25 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}}$$
Комбинаторика
/ /25*p /19*p
-2*|cos|—-| + sin|—-||
12 / 12 //
————————–
/p /11*p
2*cos|–| + cos|—-|
12/ 12 /
$$- frac{2 sin{left (frac{19 p}{12} right )} + 2 cos{left (frac{25 p}{12} right )}}{2 cos{left (frac{p}{12} right )} + cos{left (frac{11 p}{12} right )}}$$
