Дано
$$cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}} + sin{left (x right )}$$
Подстановка условия
$$cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}} + sin{left (x right )}$$
cos(5*(1/4)) – cos((1/4))/sin(5*(1/4)) + sin((1/4))
$$cos{left (5 (1/4) right )} – frac{cos{left ((1/4) right )}}{sin{left (5 (1/4) right )}} + sin{left ((1/4) right )}$$
cos(5/4) – cos(1/4)/sin(5/4) + sin(1/4)
$$- frac{cos{left (frac{1}{4} right )}}{sin{left (frac{5}{4} right )}} + cos{left (frac{5}{4} right )} + sin{left (frac{1}{4} right )}$$
-cos(1/4)/sin(5/4) + cos(5/4) + sin(1/4)
$$- frac{cos{left (frac{1}{4} right )}}{sin{left (frac{5}{4} right )}} + sin{left (frac{1}{4} right )} + cos{left (frac{5}{4} right )}$$
Степени
$$sin{left (x right )} + cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}}$$
Численный ответ
-cos(x)/sin(5*x) + cos(5*x) + sin(x)
Рациональный знаменатель
$$frac{1}{sin{left (5 x right )}} left(sin{left (x right )} sin{left (5 x right )} + sin{left (5 x right )} cos{left (5 x right )} – cos{left (x right )}right)$$
Объединение рациональных выражений
$$frac{1}{sin{left (5 x right )}} left(sin{left (x right )} sin{left (5 x right )} + sin{left (5 x right )} cos{left (5 x right )} – cos{left (x right )}right)$$
Общее упрощение
cos(x)
– ——– + cos(5*x) + sin(x)
sin(5*x)
$$sin{left (x right )} + cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}}$$
Соберем выражение
$$sin{left (x right )} + cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}}$$
-cos(x)*csc(5*x) + cos(5*x) + sin(x)
$$sin{left (x right )} – cos{left (x right )} csc{left (5 x right )} + cos{left (5 x right )}$$
Общий знаменатель
cos(x)
– ——– + cos(5*x) + sin(x)
sin(5*x)
$$sin{left (x right )} + cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}}$$
Тригонометрическая часть
cos(x)
– ——– + cos(5*x) + sin(x)
sin(5*x)
$$sin{left (x right )} + cos{left (5 x right )} – frac{cos{left (x right )}}{sin{left (5 x right )}}$$
Комбинаторика
-cos(x) + cos(5*x)*sin(5*x) + sin(x)*sin(5*x)
———————————————
sin(5*x)
$$frac{1}{sin{left (5 x right )}} left(sin{left (x right )} sin{left (5 x right )} + sin{left (5 x right )} cos{left (5 x right )} – cos{left (x right )}right)$$
Раскрыть выражение
5 cos(x) 3 2 4
cos (x) – ———————————————– – 10*cos (x)*sin (x) + 5*sin (x)*cos(x) + sin(x)
5 2 3 4
sin (x) – 10*cos (x)*sin (x) + 5*cos (x)*sin(x)
$$5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + sin{left (x right )} + cos^{5}{left (x right )} – frac{cos{left (x right )}}{sin^{5}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )}}$$
