Дано
$$frac{1}{2} left(a + pright) sin{left (a – frac{p}{2} right )} cos{left (- a right )} + cos{left (- a + frac{3 p}{2} right )} + 1$$
Подстановка условия
$$frac{1}{2} left(a + pright) sin{left (a – frac{p}{2} right )} cos{left (- a right )} + cos{left (- a + frac{3 p}{2} right )} + 1$$
cos((3*p)/2 – (-2)) + (((p + (-2))/2)*sin((-2) – p/2))*cos(-(-2)) + 1
$$frac{1}{2} left((-2) + pright) sin{left ((-2) – frac{p}{2} right )} cos{left (- (-2) right )} + cos{left (- (-2) + frac{3 p}{2} right )} + 1$$
cos((3*p)/2 – (-2)) + (((p – 2)/2)*sin(-2 – p/2))*cos(-(-2)) + 1
$$frac{1}{2} left(p – 2right) sin{left (- frac{p}{2} – 2 right )} cos{left (- -2 right )} + cos{left (frac{3 p}{2} – -2 right )} + 1$$
1 – (-1 + p/2)*cos(2)*sin(2 + p/2) + cos(2 + 3*p/2)
$$- left(frac{p}{2} – 1right) sin{left (frac{p}{2} + 2 right )} cos{left (2 right )} + cos{left (frac{3 p}{2} + 2 right )} + 1$$
Степени
$$left(frac{a}{2} + frac{p}{2}right) sin{left (a – frac{p}{2} right )} cos{left (a right )} + cos{left (a – frac{3 p}{2} right )} + 1$$
Численный ответ
1.0 + 0.5*(a + p)*cos(-a)*sin(a – p/2) + cos((3*p)/2 – a)
Рациональный знаменатель
$$frac{1}{2} left(a sin{left (a – frac{p}{2} right )} cos{left (a right )} + p sin{left (a – frac{p}{2} right )} cos{left (a right )} + 2 cos{left (a – frac{3 p}{2} right )} + 2right)$$
Объединение рациональных выражений
$$frac{1}{2} left(left(a + pright) sin{left (frac{1}{2} left(2 a – pright) right )} cos{left (a right )} + 2 cos{left (frac{1}{2} left(- 2 a + 3 pright) right )} + 2right)$$
Общее упрощение
/ p
(a + p)*cos(a)*sin|a – -|
2/ / 3*p
1 + ————————- + cos|a – —|
2 2 /
$$frac{1}{2} left(a + pright) sin{left (a – frac{p}{2} right )} cos{left (a right )} + cos{left (a – frac{3 p}{2} right )} + 1$$
Соберем выражение
$$- frac{a}{4} sin{left (frac{p}{2} right )} + frac{a}{4} sin{left (2 a – frac{p}{2} right )} + frac{p}{4} left(- sin{left (frac{p}{2} right )} + sin{left (2 a – frac{p}{2} right )}right) + cos{left (a – frac{3 p}{2} right )} + 1$$
Общий знаменатель
/ p / p
a*cos(-a)*sin|a – -| p*cos(-a)*sin|a – -|
2/ 2/ / 3*p
1 + ——————– + ——————– + cos|a – —|
2 2 2 /
$$frac{a}{2} sin{left (a – frac{p}{2} right )} cos{left (- a right )} + frac{p}{2} sin{left (a – frac{p}{2} right )} cos{left (- a right )} + cos{left (a – frac{3 p}{2} right )} + 1$$
Тригонометрическая часть
/a p / p / 3*p
1 + |- + -|*cos(a)*sin|a – -| + cos|a – —|
2 2/ 2/ 2 /
$$left(frac{a}{2} + frac{p}{2}right) sin{left (a – frac{p}{2} right )} cos{left (a right )} + cos{left (a – frac{3 p}{2} right )} + 1$$
Комбинаторика
/ 3*p / p / p
2 + 2*cos|a – —| + a*cos(a)*sin|a – -| + p*cos(a)*sin|a – -|
2 / 2/ 2/
————————————————————–
2
$$frac{1}{2} left(a sin{left (a – frac{p}{2} right )} cos{left (a right )} + p sin{left (a – frac{p}{2} right )} cos{left (a right )} + 2 cos{left (a – frac{3 p}{2} right )} + 2right)$$
Раскрыть выражение
/ /p /p
(a + p)*|cos(a)*sin|-| – cos|-|*sin(a)|*cos(a)
/3*p /3*p 2/ 2/ /
1 + cos(a)*cos|—| + sin(a)*sin|—| – ———————————————-
2 / 2 / 2
$$- frac{1}{2} left(a + pright) left(- sin{left (a right )} cos{left (frac{p}{2} right )} + sin{left (frac{p}{2} right )} cos{left (a right )}right) cos{left (a right )} + sin{left (a right )} sin{left (frac{3 p}{2} right )} + cos{left (a right )} cos{left (frac{3 p}{2} right )} + 1$$
