Дано
$$frac{cos{left (- 2 p + 4 x right )} + 1 + cos{left (- frac{p}{2} + 4 x right )}}{cos{left (p + 4 x right )} + 1 – cos{left (frac{3 p}{2} + 4 x right )}}$$
Степени
$$frac{cos{left (frac{p}{2} – 4 x right )} + cos{left (2 p – 4 x right )} + 1}{cos{left (p + 4 x right )} – cos{left (frac{3 p}{2} + 4 x right )} + 1}$$
Численный ответ
(1.0 + cos(4*x – 2*p) + cos(4*x – p/2))/(1.0 – cos(4*x + (3*p)/2) + cos(4*x + p))
Рациональный знаменатель
$$frac{cos{left (frac{p}{2} – 4 x right )} + cos{left (2 p – 4 x right )} + 1}{cos{left (p + 4 x right )} – cos{left (frac{3 p}{2} + 4 x right )} + 1}$$
Объединение рациональных выражений
$$frac{cos{left (2 left(- p + 2 xright) right )} + cos{left (frac{1}{2} left(- p + 8 xright) right )} + 1}{cos{left (p + 4 x right )} – cos{left (frac{1}{2} left(3 p + 8 xright) right )} + 1}$$
Общее упрощение
/p
1 + cos|- – 4*x| + cos(-4*x + 2*p)
2 /
———————————-
/ 3*p
1 – cos|4*x + —| + cos(p + 4*x)
2 /
$$frac{cos{left (frac{p}{2} – 4 x right )} + cos{left (2 p – 4 x right )} + 1}{cos{left (p + 4 x right )} – cos{left (frac{3 p}{2} + 4 x right )} + 1}$$
Соберем выражение
$$- frac{cos{left (frac{p}{2} – 4 x right )}}{- cos{left (p + 4 x right )} + cos{left (frac{3 p}{2} + 4 x right )} – 1} – frac{cos{left (2 p – 4 x right )}}{- cos{left (p + 4 x right )} + cos{left (frac{3 p}{2} + 4 x right )} – 1} – frac{1}{- cos{left (p + 4 x right )} + cos{left (frac{3 p}{2} + 4 x right )} – 1}$$
/ p
1 + cos(4*x – 2*p) + cos|4*x – -|
2/
———————————
/ 3*p
1 – cos|4*x + —| + cos(4*x + p)
2 /
$$frac{cos{left (- 2 p + 4 x right )} + cos{left (- frac{p}{2} + 4 x right )} + 1}{cos{left (p + 4 x right )} – cos{left (frac{3 p}{2} + 4 x right )} + 1}$$
Комбинаторика
/ /p
-|1 + cos|- – 4*x| + cos(-4*x + 2*p)|
2 / /
————————————–
/ 3*p
-1 – cos(p + 4*x) + cos|4*x + —|
2 /
$$- frac{cos{left (frac{p}{2} – 4 x right )} + cos{left (2 p – 4 x right )} + 1}{- cos{left (p + 4 x right )} + cos{left (frac{3 p}{2} + 4 x right )} – 1}$$
Общий знаменатель
/ /p
-|1 + cos|- – 4*x| + cos(-4*x + 2*p)|
2 / /
————————————–
/ 3*p
-1 – cos(p + 4*x) + cos|4*x + —|
2 /
$$- frac{cos{left (frac{p}{2} – 4 x right )} + cos{left (2 p – 4 x right )} + 1}{- cos{left (p + 4 x right )} + cos{left (frac{3 p}{2} + 4 x right )} – 1}$$
Тригонометрическая часть
/p
1 + cos|- – 4*x| + cos(4*x – 2*p)
2 /
———————————
/ 3*p
1 – cos|4*x + —| + cos(4*x + p)
2 /
$$frac{cos{left (frac{p}{2} – 4 x right )} + cos{left (- 2 p + 4 x right )} + 1}{cos{left (p + 4 x right )} – cos{left (frac{3 p}{2} + 4 x right )} + 1}$$
Раскрыть выражение
/p /p
1 + cos|-|*cos(4*x) + cos(2*p)*cos(4*x) + sin|-|*sin(4*x) + sin(2*p)*sin(4*x)
2/ 2/
—————————————————————————–
/3*p /3*p
1 + cos(p)*cos(4*x) + sin(4*x)*sin|—| – cos(4*x)*cos|—| – sin(p)*sin(4*x)
2 / 2 /
$$frac{sin{left (frac{p}{2} right )} sin{left (4 x right )} + sin{left (2 p right )} sin{left (4 x right )} + cos{left (frac{p}{2} right )} cos{left (4 x right )} + cos{left (2 p right )} cos{left (4 x right )} + 1}{- sin{left (p right )} sin{left (4 x right )} + sin{left (frac{3 p}{2} right )} sin{left (4 x right )} + cos{left (p right )} cos{left (4 x right )} – cos{left (frac{3 p}{2} right )} cos{left (4 x right )} + 1}$$
