Дано
$$frac{440 cos{left (pi m right )}}{n pi^{2} m} cos{left (pi n right )}$$
Подстановка условия
$$frac{440 cos{left (pi m right )}}{n pi^{2} m} cos{left (pi n right )}$$
((440*cos(pi*(1/4)))*cos(pi*n))/((pi^2*(1/4))*n)
$$frac{440 cos{left (pi (1/4) right )}}{n pi^{2} (1/4)} cos{left (pi n right )}$$
((440*cos(pi/4))*cos(pi*n))/((pi^2/4)*n)
$$frac{1}{n frac{pi^{2}}{4}} 440 cos{left (frac{pi}{4} right )} cos{left (pi n right )}$$
880*sqrt(2)*cos(pi*n)/(pi^2*n)
$$frac{880 sqrt{2}}{pi^{2} n} cos{left (pi n right )}$$
Степени
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Численный ответ
44.5813208026286*cos(pi*m)*cos(pi*n)/(m*n)
Рациональный знаменатель
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Объединение рациональных выражений
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Общее упрощение
440*cos(pi*m)*cos(pi*n)
———————–
2
pi *m*n
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Соберем выражение
$$frac{220}{pi^{2} m n} cos{left (pi m – pi n right )} + frac{220}{pi^{2} m n} cos{left (pi m + pi n right )}$$
440*cos(pi*m)*cos(pi*n)
———————–
2
pi *m*n
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Общий знаменатель
440*cos(pi*m)*cos(pi*n)
———————–
2
pi *m*n
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Тригонометрическая часть
440*cos(pi*m)*cos(pi*n)
———————–
2
pi *m*n
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Комбинаторика
440*cos(pi*m)*cos(pi*n)
———————–
2
pi *m*n
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$
Раскрыть выражение
440*cos(pi*m)*cos(pi*n)
———————–
2
pi *m*n
$$frac{440 cos{left (pi m right )}}{pi^{2} m n} cos{left (pi n right )}$$