Дано
$$cos{left (3 x right )} cos{left (6 x right )} cos{left (12 x right )} cos{left (24 x right )}$$
Подстановка условия
$$cos{left (3 x right )} cos{left (6 x right )} cos{left (12 x right )} cos{left (24 x right )}$$
((cos(3*(2))*cos(6*(2)))*cos(12*(2)))*cos(24*(2))
$$cos{left (3 (2) right )} cos{left (6 (2) right )} cos{left (12 (2) right )} cos{left (24 (2) right )}$$
((cos(3*2)*cos(6*2))*cos(12*2))*cos(24*2)
$$cos{left (2 cdot 3 right )} cos{left (2 cdot 6 right )} cos{left (2 cdot 12 right )} cos{left (2 cdot 24 right )}$$
cos(6)*cos(12)*cos(24)*cos(48)
$$cos{left (6 right )} cos{left (12 right )} cos{left (24 right )} cos{left (48 right )}$$
Численный ответ
cos(3*x)*cos(6*x)*cos(12*x)*cos(24*x)
Соберем выражение
$$frac{1}{8} cos{left (3 x right )} + frac{1}{8} cos{left (9 x right )} + frac{1}{8} cos{left (15 x right )} + frac{1}{8} cos{left (21 x right )} + frac{1}{8} cos{left (27 x right )} + frac{1}{8} cos{left (33 x right )} + frac{1}{8} cos{left (39 x right )} + frac{1}{8} cos{left (45 x right )}$$
Раскрыть выражение
/ 3 2 / 6 6 4 2 2 4 / 12 12 6 6 2 10 10 2 4 8 8 4 / 24 24 10 14 14 10 6 18 18 6 2 22 22 2 4 20 20 4 8 16 16 8 12 12
cos (x) – 3*sin (x)*cos(x)/*cos (x) – sin (x) – 15*cos (x)*sin (x) + 15*cos (x)*sin (x)/*cos (x) + sin (x) – 924*cos (x)*sin (x) – 66*cos (x)*sin (x) – 66*cos (x)*sin (x) + 495*cos (x)*sin (x) + 495*cos (x)*sin (x)/*cos (x) + sin (x) – 1961256*cos (x)*sin (x) – 1961256*cos (x)*sin (x) – 134596*cos (x)*sin (x) – 134596*cos (x)*sin (x) – 276*cos (x)*sin (x) – 276*cos (x)*sin (x) + 10626*cos (x)*sin (x) + 10626*cos (x)*sin (x) + 735471*cos (x)*sin (x) + 735471*cos (x)*sin (x) + 2704156*cos (x)*sin (x)/
$$left(- 3 sin^{2}{left (x right )} cos{left (x right )} + cos^{3}{left (x right )}right) left(- sin^{6}{left (x right )} + 15 sin^{4}{left (x right )} cos^{2}{left (x right )} – 15 sin^{2}{left (x right )} cos^{4}{left (x right )} + cos^{6}{left (x right )}right) left(sin^{12}{left (x right )} – 66 sin^{10}{left (x right )} cos^{2}{left (x right )} + 495 sin^{8}{left (x right )} cos^{4}{left (x right )} – 924 sin^{6}{left (x right )} cos^{6}{left (x right )} + 495 sin^{4}{left (x right )} cos^{8}{left (x right )} – 66 sin^{2}{left (x right )} cos^{10}{left (x right )} + cos^{12}{left (x right )}right) left(sin^{24}{left (x right )} – 276 sin^{22}{left (x right )} cos^{2}{left (x right )} + 10626 sin^{20}{left (x right )} cos^{4}{left (x right )} – 134596 sin^{18}{left (x right )} cos^{6}{left (x right )} + 735471 sin^{16}{left (x right )} cos^{8}{left (x right )} – 1961256 sin^{14}{left (x right )} cos^{10}{left (x right )} + 2704156 sin^{12}{left (x right )} cos^{12}{left (x right )} – 1961256 sin^{10}{left (x right )} cos^{14}{left (x right )} + 735471 sin^{8}{left (x right )} cos^{16}{left (x right )} – 134596 sin^{6}{left (x right )} cos^{18}{left (x right )} + 10626 sin^{4}{left (x right )} cos^{20}{left (x right )} – 276 sin^{2}{left (x right )} cos^{22}{left (x right )} + cos^{24}{left (x right )}right)$$
