Дано
$$frac{sin{left (2 a right )} – sin{left (3 a right )} + sin{left (4 a right )}}{cos{left (2 a right )} – cos{left (3 a right )} + cos{left (4 a right )}}$$
Подстановка условия
$$frac{sin{left (2 a right )} – sin{left (3 a right )} + sin{left (4 a right )}}{cos{left (2 a right )} – cos{left (3 a right )} + cos{left (4 a right )}}$$
(sin(2*(-2)) – sin(3*(-2)) + sin(4*(-2)))/(cos(2*(-2)) – cos(3*(-2)) + cos(4*(-2)))
$$frac{sin{left (2 (-2) right )} – sin{left (3 (-2) right )} + sin{left (4 (-2) right )}}{cos{left (2 (-2) right )} – cos{left (3 (-2) right )} + cos{left (4 (-2) right )}}$$
(sin(2*(-2)) – sin(3*(-2)) + sin(4*(-2)))/(cos(2*(-2)) – cos(3*(-2)) + cos(4*(-2)))
$$frac{sin{left (-2 cdot 4 right )} + – sin{left (-2 cdot 3 right )} + sin{left (-2 cdot 2 right )}}{- cos{left (-2 cdot 3 right )} + cos{left (-2 cdot 2 right )} + cos{left (-2 cdot 4 right )}}$$
(-sin(4) – sin(8) + sin(6))/(-cos(6) + cos(4) + cos(8))
$$frac{- sin{left (8 right )} + sin{left (6 right )} – sin{left (4 right )}}{- cos{left (6 right )} + cos{left (4 right )} + cos{left (8 right )}}$$
Численный ответ
(-sin(3*a) + sin(2*a) + sin(4*a))/(-cos(3*a) + cos(2*a) + cos(4*a))
Соберем выражение
$$frac{sin{left (2 a right )}}{cos{left (2 a right )} – cos{left (3 a right )} + cos{left (4 a right )}} – frac{sin{left (3 a right )}}{cos{left (2 a right )} – cos{left (3 a right )} + cos{left (4 a right )}} + frac{sin{left (4 a right )}}{cos{left (2 a right )} – cos{left (3 a right )} + cos{left (4 a right )}}$$
Раскрыть выражение
3 3 2 3
sin (a) – 4*sin (a)*cos(a) – 3*cos (a)*sin(a) + 2*cos(a)*sin(a) + 4*cos (a)*sin(a)
————————————————————————————–
2 4 4 3 2 2 2 2
cos (a) + cos (a) + sin (a) – cos (a) – sin (a) – 6*cos (a)*sin (a) + 3*sin (a)*cos(a)
$$frac{- 4 sin^{3}{left (a right )} cos{left (a right )} + sin^{3}{left (a right )} + 4 sin{left (a right )} cos^{3}{left (a right )} – 3 sin{left (a right )} cos^{2}{left (a right )} + 2 sin{left (a right )} cos{left (a right )}}{sin^{4}{left (a right )} – 6 sin^{2}{left (a right )} cos^{2}{left (a right )} + 3 sin^{2}{left (a right )} cos{left (a right )} – sin^{2}{left (a right )} + cos^{4}{left (a right )} – cos^{3}{left (a right )} + cos^{2}{left (a right )}}$$