Дано
$$frac{-140 cdot 39 sin{left (t right )} sin{left (2 t right )} – 2730 cos{left (t right )} cos{left (2 t right )}}{left(1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}right)^{frac{3}{2}}}$$
Подстановка условия
$$frac{-140 cdot 39 sin{left (t right )} sin{left (2 t right )} – 2730 cos{left (t right )} cos{left (2 t right )}}{left(1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}right)^{frac{3}{2}}}$$
(((39*sin((-3)))*(-140))*sin(2*(-3)) – (39*cos((-3)))*70*cos(2*(-3)))/(1521*sin((-3))^2 + 4900*cos(2*(-3))^2)^(3/2)
$$frac{-140 cdot 39 sin{left ((-3) right )} sin{left (2 (-3) right )} – 2730 cos{left ((-3) right )} cos{left (2 (-3) right )}}{left(1521 sin^{2}{left ((-3) right )} + 4900 cos^{2}{left (2 (-3) right )}right)^{frac{3}{2}}}$$
(((39*sin(-3))*(-140))*sin(2*(-3)) – (39*cos(-3))*70*cos(2*(-3)))/(1521*sin(-3)^2 + 4900*cos(2*(-3))^2)^(3/2)
$$frac{-140 cdot 39 sin{left (-3 right )} sin{left (-3 cdot 2 right )} – 2730 cos{left (-3 right )} cos{left (-3 cdot 2 right )}}{left(1521 sin^{2}{left (-3 right )} + 4900 cos^{2}{left (-3 cdot 2 right )}right)^{frac{3}{2}}}$$
(-5460*sin(3)*sin(6) – 2730*cos(3)*cos(6))/(1521*sin(3)^2 + 4900*cos(6)^2)^(3/2)
$$frac{- 5460 sin{left (3 right )} sin{left (6 right )} – 2730 cos{left (3 right )} cos{left (6 right )}}{left(1521 sin^{2}{left (3 right )} + 4900 cos^{2}{left (6 right )}right)^{frac{3}{2}}}$$
Степени
$$frac{- 5460 sin{left (t right )} sin{left (2 t right )} – 2730 cos{left (t right )} cos{left (2 t right )}}{left(1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}right)^{frac{3}{2}}}$$
Численный ответ
(4900.0*cos(2*t)^2 + 1521.0*sin(t)^2)^(-1.5)*(-2730.0*cos(t)*cos(2*t) – 5460.0*sin(t)*sin(2*t))
Рациональный знаменатель
$$- frac{2730 left(2 sin{left (t right )} sin{left (2 t right )} + cos{left (t right )} cos{left (2 t right )}right) sqrt{1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}}}{2313441 sin^{4}{left (t right )} + 14905800 sin^{2}{left (t right )} cos^{2}{left (2 t right )} + 24010000 cos^{4}{left (2 t right )}}$$
Объединение рациональных выражений
$$frac{- 5460 sin{left (t right )} sin{left (2 t right )} – 2730 cos{left (t right )} cos{left (2 t right )}}{left(1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}right)^{frac{3}{2}}}$$
Общее упрощение
1365*(-3*cos(t) + cos(3*t))
—————————————–
3/2
/ 2 4
4900 – 18079*sin (t) + 19600*sin (t)/
$$frac{- 4095 cos{left (t right )} + 1365 cos{left (3 t right )}}{left(19600 sin^{4}{left (t right )} – 18079 sin^{2}{left (t right )} + 4900right)^{frac{3}{2}}}$$
Соберем выражение
$$- frac{8190 sqrt{2} cos{left (t right )}}{left(- 1521 cos{left (2 t right )} + 4900 cos{left (4 t right )} + 6421right)^{frac{3}{2}}} + frac{2730 sqrt{2} cos{left (3 t right )}}{left(- 1521 cos{left (2 t right )} + 4900 cos{left (4 t right )} + 6421right)^{frac{3}{2}}}$$
Общий знаменатель
-(2730*cos(t)*cos(2*t) + 5460*sin(t)*sin(2*t))
—————————————————————————————————
_______________________________ _______________________________
/ 2 2 2 / 2 2 2
1521*/ 1521*sin (t) + 4900*cos (2*t) *sin (t) + 4900*/ 1521*sin (t) + 4900*cos (2*t) *cos (2*t)
$$- frac{5460 sin{left (t right )} sin{left (2 t right )} + 2730 cos{left (t right )} cos{left (2 t right )}}{1521 sqrt{1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}} sin^{2}{left (t right )} + 4900 sqrt{1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}} cos^{2}{left (2 t right )}}$$
Тригонометрическая часть
1365*(-3*cos(t) + cos(3*t))
—————————————–
3/2
/ 2 4
4900 – 18079*sin (t) + 19600*sin (t)/
$$frac{- 4095 cos{left (t right )} + 1365 cos{left (3 t right )}}{left(19600 sin^{4}{left (t right )} – 18079 sin^{2}{left (t right )} + 4900right)^{frac{3}{2}}}$$
Комбинаторика
-2730*(cos(t)*cos(2*t) + 2*sin(t)*sin(2*t))
——————————————-
3/2
/ 2 2
1521*sin (t) + 4900*cos (2*t)/
$$- frac{5460 sin{left (t right )} sin{left (2 t right )} + 2730 cos{left (t right )} cos{left (2 t right )}}{left(1521 sin^{2}{left (t right )} + 4900 cos^{2}{left (2 t right )}right)^{frac{3}{2}}}$$
Раскрыть выражение
2 / 2 2
– 10920*sin (t)*cos(t) – 2730*cos (t) – sin (t)/*cos(t)
——————————————————–
3/2
/ 2
| 2 / 2 2 |
1521*sin (t) + 4900*cos (t) – sin (t)/ /
$$frac{- 2730 left(- sin^{2}{left (t right )} + cos^{2}{left (t right )}right) cos{left (t right )} – 10920 sin^{2}{left (t right )} cos{left (t right )}}{left(4900 left(- sin^{2}{left (t right )} + cos^{2}{left (t right )}right)^{2} + 1521 sin^{2}{left (t right )}right)^{frac{3}{2}}}$$
