Дано
$$frac{cos{left (3 x right )} + cos{left (5 x right )} + cos{left (7 x right )}}{sin{left (3 x right )} + sin{left (5 x right )} + sin{left (7 x right )}}$$
Подстановка условия
$$frac{cos{left (3 x right )} + cos{left (5 x right )} + cos{left (7 x right )}}{sin{left (3 x right )} + sin{left (5 x right )} + sin{left (7 x right )}}$$
(cos(3*(-1/3)) + cos(5*(-1/3)) + cos(7*(-1/3)))/(sin(3*(-1/3)) + sin(5*(-1/3)) + sin(7*(-1/3)))
$$frac{cos{left (3 (-1/3) right )} + cos{left (5 (-1/3) right )} + cos{left (7 (-1/3) right )}}{sin{left (3 (-1/3) right )} + sin{left (5 (-1/3) right )} + sin{left (7 (-1/3) right )}}$$
(cos(3*(-1)/3) + cos(5*(-1)/3) + cos(7*(-1)/3))/(sin(3*(-1)/3) + sin(5*(-1)/3) + sin(7*(-1)/3))
$$frac{cos{left (frac{-7}{3} right )} + cos{left (frac{-5}{3} right )} + cos{left (frac{-3}{3} right )}}{sin{left (frac{-5}{3} right )} + sin{left (frac{-3}{3} right )} + sin{left (frac{-7}{3} right )}}$$
(cos(1) + cos(5/3) + cos(7/3))/(-sin(1) – sin(5/3) – sin(7/3))
$$frac{cos{left (frac{7}{3} right )} + cos{left (frac{5}{3} right )} + cos{left (1 right )}}{- sin{left (frac{5}{3} right )} – sin{left (1 right )} – sin{left (frac{7}{3} right )}}$$
Численный ответ
(cos(3*x) + cos(5*x) + cos(7*x))/(sin(3*x) + sin(5*x) + sin(7*x))
Соберем выражение
$$frac{cos{left (3 x right )}}{sin{left (3 x right )} + sin{left (5 x right )} + sin{left (7 x right )}} + frac{cos{left (5 x right )}}{sin{left (3 x right )} + sin{left (5 x right )} + sin{left (7 x right )}} + frac{cos{left (7 x right )}}{sin{left (3 x right )} + sin{left (5 x right )} + sin{left (7 x right )}}$$
Раскрыть выражение
3 5 7 5 2 3 2 6 2 4 3 4
cos (x) + cos (x) + cos (x) – 21*cos (x)*sin (x) – 10*cos (x)*sin (x) – 7*sin (x)*cos(x) – 3*sin (x)*cos(x) + 5*sin (x)*cos(x) + 35*cos (x)*sin (x)
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5 3 7 4 3 2 3 2 4 6 2 5
sin (x) – sin (x) – sin (x) – 35*cos (x)*sin (x) – 10*cos (x)*sin (x) + 3*cos (x)*sin(x) + 5*cos (x)*sin(x) + 7*cos (x)*sin(x) + 21*cos (x)*sin (x)
$$frac{- 7 sin^{6}{left (x right )} cos{left (x right )} + 35 sin^{4}{left (x right )} cos^{3}{left (x right )} + 5 sin^{4}{left (x right )} cos{left (x right )} – 21 sin^{2}{left (x right )} cos^{5}{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} – 3 sin^{2}{left (x right )} cos{left (x right )} + cos^{7}{left (x right )} + cos^{5}{left (x right )} + cos^{3}{left (x right )}}{- sin^{7}{left (x right )} + 21 sin^{5}{left (x right )} cos^{2}{left (x right )} + sin^{5}{left (x right )} – 35 sin^{3}{left (x right )} cos^{4}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} – sin^{3}{left (x right )} + 7 sin{left (x right )} cos^{6}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )} + 3 sin{left (x right )} cos^{2}{left (x right )}}$$
