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