Дано
$$frac{1}{300} x cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + left(frac{1}{100} left(-1 cdot 3 x sin{left (frac{3 x}{100} right )}right) + cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}$$
Подстановка условия
$$frac{1}{300} x cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + left(frac{1}{100} left(-1 cdot 3 x sin{left (frac{3 x}{100} right )}right) + cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}$$
(((-3*(-1/3))*sin((3*(-1/3))/100))/100 + cos((3*(-1/3))/100))*sin((-1/3)/300) + (((-1/3)*cos((-1/3)/300))*cos((3*(-1/3))/100))/300
$$frac{1}{300} (-1/3) cos{left (frac{(-1/3)}{300} right )} cos{left (frac{3 (-1/3)}{100} right )} + left(frac{1}{100} left(-1 cdot 3 (-1/3) sin{left (frac{3 (-1/3)}{100} right )}right) + cos{left (frac{3 (-1/3)}{100} right )}right) sin{left (frac{(-1/3)}{300} right )}$$
(((-(-1))*sin((3*(-1)/3)/100))/100 + cos((3*(-1)/3)/100))*sin(-1/900) + ((-cos(-1/900)/3)*cos((3*(-1)/3)/100))/300
$$frac{1}{300} left(-1 frac{1}{3} cos{left (- frac{1}{900} right )} cos{left (frac{-1}{100} 1 right )}right) + left(frac{1}{100} sin{left (frac{-1}{100} 1 right )} + cos{left (frac{-1}{100} 1 right )}right) sin{left (- frac{1}{900} right )}$$
-(-sin(1/100)/100 + cos(1/100))*sin(1/900) – cos(1/100)*cos(1/900)/900
$$- frac{1}{900} cos{left (frac{1}{900} right )} cos{left (frac{1}{100} right )} – left(- frac{1}{100} sin{left (frac{1}{100} right )} + cos{left (frac{1}{100} right )}right) sin{left (frac{1}{900} right )}$$
Степени
$$frac{x}{300} cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + left(- frac{3 x}{100} sin{left (frac{3 x}{100} right )} + cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}$$
Численный ответ
(-0.03*x*sin((3*x)/100) + cos((3*x)/100))*sin(x/300) + 0.00333333333333333*x*cos(x/300)*cos((3*x)/100)
Рациональный знаменатель
$$frac{1}{300} left(- 9 x sin{left (frac{x}{300} right )} sin{left (frac{3 x}{100} right )} + x cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + 300 sin{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )}right)$$
Объединение рациональных выражений
$$frac{1}{300} left(x cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + 3 left(- 3 x sin{left (frac{3 x}{100} right )} + 100 cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}right)$$
Общее упрощение
/ /3*x /3*x / x / x /3*x
|- 100*cos|—| + 3*x*sin|—||*sin|—| x*cos|—|*cos|—|
100/ 100// 300/ 300/ 100/
– —————————————- + ——————-
100 300
$$frac{x}{300} cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} – frac{1}{100} left(3 x sin{left (frac{3 x}{100} right )} – 100 cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}$$
Соберем выражение
$$frac{x}{200} left(- 3 cos{left (frac{2 x}{75} right )} + 3 cos{left (frac{x}{30} right )}right) + frac{x}{600} left(cos{left (frac{2 x}{75} right )} + cos{left (frac{x}{30} right )}right) – frac{1}{2} sin{left (frac{2 x}{75} right )} + frac{1}{2} sin{left (frac{x}{30} right )}$$
Общий знаменатель
/ x /3*x / x /3*x
3*x*sin|—|*sin|—| x*cos|—|*cos|—|
/3*x / x 300/ 100/ 300/ 100/
cos|—|*sin|—| – ——————— + ——————-
100/ 300/ 100 300
$$- frac{3 x}{100} sin{left (frac{x}{300} right )} sin{left (frac{3 x}{100} right )} + frac{x}{300} cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + sin{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )}$$
Тригонометрическая часть
/ /3*x /3*x / x
| 3*x*sin|—| | x*cos|—|*cos|—|
| 100/ /3*x| / x 100/ 300/
|- ———— + cos|—||*sin|—| + ——————-
100 100// 300/ 300
$$frac{x}{300} cos{left (frac{3 x}{100} right )} cos{left (frac{x}{300} right )} + left(- frac{3 x}{100} sin{left (frac{3 x}{100} right )} + cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}$$
Комбинаторика
/3*x / x / x /3*x / x /3*x
300*cos|—|*sin|—| + x*cos|—|*cos|—| – 9*x*sin|—|*sin|—|
100/ 300/ 300/ 100/ 300/ 100/
——————————————————————-
300
$$frac{1}{300} left(- 9 x sin{left (frac{x}{300} right )} sin{left (frac{3 x}{100} right )} + x cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + 300 sin{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )}right)$$
Раскрыть выражение
/ /3*x / x /3*x
| 3*x*sin|—| | x*cos|—|*cos|—|
| 100/ /3*x| / x 300/ 100/
|- ———— + cos|—||*sin|—| + ——————-
100 100// 300/ 300
$$frac{x}{300} cos{left (frac{x}{300} right )} cos{left (frac{3 x}{100} right )} + left(- frac{3 x}{100} sin{left (frac{3 x}{100} right )} + cos{left (frac{3 x}{100} right )}right) sin{left (frac{x}{300} right )}$$
