Дано
$$frac{frac{1}{5} sqrt{5} cdot 5 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}{3 sin{left (x right )} – 2 cos{left (x right )}} left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right)$$
Подстановка условия
$$frac{frac{1}{5} sqrt{5} cdot 5 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}{3 sin{left (x right )} – 2 cos{left (x right )}} left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right)$$
((((5*sqrt(3*sin((-3)) – 2*cos((-3))))*sqrt(5))/5)*(sin((-3))/5 + (3*cos((-3)))/10))/(3*sin((-3)) – 2*cos((-3)))
$$frac{frac{1}{5} sqrt{5} cdot 5 sqrt{3 sin{left ((-3) right )} – 2 cos{left ((-3) right )}}}{3 sin{left ((-3) right )} – 2 cos{left ((-3) right )}} left(frac{1}{5} sin{left ((-3) right )} + frac{3}{10} cos{left ((-3) right )}right)$$
((((5*sqrt(3*sin(-3) – 2*cos(-3)))*sqrt(5))/5)*(sin(-3)/5 + (3*cos(-3))/10))/(3*sin(-3) – 2*cos(-3))
$$frac{frac{1}{5} sqrt{5} cdot 5 sqrt{3 sin{left (-3 right )} – 2 cos{left (-3 right )}}}{3 sin{left (-3 right )} – 2 cos{left (-3 right )}} left(frac{3}{10} cos{left (-3 right )} + frac{1}{5} sin{left (-3 right )}right)$$
sqrt(5)*(-sin(3)/5 + 3*cos(3)/10)/sqrt(-3*sin(3) – 2*cos(3))
$$frac{sqrt{5} left(frac{3}{10} cos{left (3 right )} – frac{1}{5} sin{left (3 right )}right)}{sqrt{- 3 sin{left (3 right )} – 2 cos{left (3 right )}}}$$
Степени
$$frac{left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right) sqrt{15 sin{left (x right )} – 10 cos{left (x right )}}}{3 sin{left (x right )} – 2 cos{left (x right )}}$$
___ /sin(x) 3*cos(x)
/ 5 *|—— + ——–|
5 10 /
————————-
______________________
/ -2*cos(x) + 3*sin(x)
$$frac{sqrt{5} left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right)}{sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Численный ответ
2.23606797749979*(3.0*sin(x) – 2.0*cos(x))^(-0.5)*(0.3*cos(x) + 0.2*sin(x))
Рациональный знаменатель
$$frac{5 sqrt{5} sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}{750 sin{left (x right )} – 500 cos{left (x right )}} left(10 sin{left (x right )} + 15 cos{left (x right )}right)$$
Объединение рациональных выражений
$$frac{sqrt{5} left(2 sin{left (x right )} + 3 cos{left (x right )}right)}{10 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Общее упрощение
___
/ 5 *(2*sin(x) + 3*cos(x))
—————————
______________________
10*/ -2*cos(x) + 3*sin(x)
$$frac{sqrt{5} left(2 sin{left (x right )} + 3 cos{left (x right )}right)}{10 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Соберем выражение
$$frac{sqrt{5} left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right)}{sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
___ ___
/ 5 *sin(x) 3*/ 5 *cos(x)
————————– + —————————
______________________ ______________________
5*/ -2*cos(x) + 3*sin(x) 10*/ -2*cos(x) + 3*sin(x)
$$frac{sqrt{5} sin{left (x right )}}{5 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}} + frac{3 sqrt{5} cos{left (x right )}}{10 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Общий знаменатель
___ ___
2*/ 5 *sin(x) + 3*/ 5 *cos(x)
——————————-
______________________
10*/ -2*cos(x) + 3*sin(x)
$$frac{2 sqrt{5} sin{left (x right )} + 3 sqrt{5} cos{left (x right )}}{10 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Тригонометрическая часть
___ /sin(x) 3*cos(x)
/ 5 *|—— + ——–|
5 10 /
————————-
______________________
/ -2*cos(x) + 3*sin(x)
$$frac{sqrt{5} left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right)}{sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Комбинаторика
___
/ 5 *(2*sin(x) + 3*cos(x))
—————————
______________________
10*/ -2*cos(x) + 3*sin(x)
$$frac{sqrt{5} left(2 sin{left (x right )} + 3 cos{left (x right )}right)}{10 sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
Раскрыть выражение
___ /sin(x) 3*cos(x)
/ 5 *|—— + ——–|
5 10 /
————————-
______________________
/ -2*cos(x) + 3*sin(x)
$$frac{sqrt{5} left(frac{1}{5} sin{left (x right )} + frac{3}{10} cos{left (x right )}right)}{sqrt{3 sin{left (x right )} – 2 cos{left (x right )}}}$$
