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