Дано
$$frac{-1 cdot 20 cos{left (10 x right )}}{sin{left (10 x right )} sin^{2}{left (10 x right )}}$$
Подстановка условия
$$frac{-1 cdot 20 cos{left (10 x right )}}{sin{left (10 x right )} sin^{2}{left (10 x right )}}$$
(-20*cos(10*(-2)))/(sin(10*(-2))*sin(10*(-2))^2)
$$frac{-1 cdot 20 cos{left (10 (-2) right )}}{sin{left (10 (-2) right )} sin^{2}{left (10 (-2) right )}}$$
(-20*cos(10*(-2)))/(sin(10*(-2))*sin(10*(-2))^2)
$$frac{-1 cdot 20 cos{left (-2 cdot 10 right )}}{sin{left (-2 cdot 10 right )} sin^{2}{left (-2 cdot 10 right )}}$$
$$frac{20 cos{left (20 right )}}{sin^{3}{left (20 right )}}$$
Степени
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Численный ответ
-20.0*cos(10*x)/sin(10*x)^3
Рациональный знаменатель
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Объединение рациональных выражений
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Общее упрощение
-20*cos(10*x)
————-
3
sin (10*x)
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Соберем выражение
$$- 20 cot{left (10 x right )} csc^{2}{left (10 x right )}$$
-20*cos(10*x)
————-
3
sin (10*x)
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Общий знаменатель
-20*cos(10*x)
————-
3
sin (10*x)
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Тригонометрическая часть
-20*cos(10*x)
————-
3
sin (10*x)
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Комбинаторика
-20*cos(10*x)
————-
3
sin (10*x)
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
Раскрыть выражение
10 10 6 4 2 8 8 2 4 6
– 20*cos (x) + 20*sin (x) – 4200*cos (x)*sin (x) – 900*cos (x)*sin (x) + 900*cos (x)*sin (x) + 4200*cos (x)*sin (x)
———————————————————————————————————————
3
/ 3 7 7 3 9 9 5 5
– 120*cos (x)*sin (x) – 120*cos (x)*sin (x) + 10*cos (x)*sin(x) + 10*sin (x)*cos(x) + 252*cos (x)*sin (x)/
$$frac{20 sin^{10}{left (x right )} – 900 sin^{8}{left (x right )} cos^{2}{left (x right )} + 4200 sin^{6}{left (x right )} cos^{4}{left (x right )} – 4200 sin^{4}{left (x right )} cos^{6}{left (x right )} + 900 sin^{2}{left (x right )} cos^{8}{left (x right )} – 20 cos^{10}{left (x right )}}{left(10 sin^{9}{left (x right )} cos{left (x right )} – 120 sin^{7}{left (x right )} cos^{3}{left (x right )} + 252 sin^{5}{left (x right )} cos^{5}{left (x right )} – 120 sin^{3}{left (x right )} cos^{7}{left (x right )} + 10 sin{left (x right )} cos^{9}{left (x right )}right)^{3}}$$
-20*cos(10*x)
————-
3
sin (10*x)
$$- frac{20 cos{left (10 x right )}}{sin^{3}{left (10 x right )}}$$
