Дано
$$11 sin^{2}{left (21 x right )} + 14 cos^{2}{left (21 x right )}$$
Подстановка условия
$$11 sin^{2}{left (21 x right )} + 14 cos^{2}{left (21 x right )}$$
14*cos(21*(-1/4))^2 + 11*sin(21*(-1/4))^2
$$11 sin^{2}{left (21 (-1/4) right )} + 14 cos^{2}{left (21 (-1/4) right )}$$
14*cos(21*(-1)/4)^2 + 11*sin(21*(-1)/4)^2
$$14 cos^{2}{left (frac{-21}{4} right )} + 11 sin^{2}{left (frac{-21}{4} right )}$$
11*sin(21/4)^2 + 14*cos(21/4)^2
$$14 cos^{2}{left (frac{21}{4} right )} + 11 sin^{2}{left (frac{21}{4} right )}$$
Численный ответ
14.0*cos(21*x)^2 + 11.0*sin(21*x)^2
Общее упрощение
$$- 3 sin^{2}{left (21 x right )} + 14$$
Соберем выражение
$$frac{3}{2} cos{left (42 x right )} + frac{25}{2}$$
Тригонометрическая часть
$$- 3 sin^{2}{left (21 x right )} + 14$$
Раскрыть выражение
2 2
/ 21 10 11 14 7 6 15 18 3 2 19 20 4 17 16 5 8 13 12 9 / 21 11 10 7 14 15 6 3 18 19 2 20 17 4 5 16 13 8 9 12
11*sin (x) – 352716*cos (x)*sin (x) – 116280*cos (x)*sin (x) – 54264*cos (x)*sin (x) – 1330*cos (x)*sin (x) – 210*cos (x)*sin (x) + 21*cos (x)*sin(x) + 5985*cos (x)*sin (x) + 20349*cos (x)*sin (x) + 203490*cos (x)*sin (x) + 293930*cos (x)*sin (x)/ + 14*cos (x) – 352716*cos (x)*sin (x) – 116280*cos (x)*sin (x) – 54264*cos (x)*sin (x) – 1330*cos (x)*sin (x) – 210*cos (x)*sin (x) + 21*sin (x)*cos(x) + 5985*cos (x)*sin (x) + 20349*cos (x)*sin (x) + 203490*cos (x)*sin (x) + 293930*cos (x)*sin (x)/
$$14 left(21 sin^{20}{left (x right )} cos{left (x right )} – 1330 sin^{18}{left (x right )} cos^{3}{left (x right )} + 20349 sin^{16}{left (x right )} cos^{5}{left (x right )} – 116280 sin^{14}{left (x right )} cos^{7}{left (x right )} + 293930 sin^{12}{left (x right )} cos^{9}{left (x right )} – 352716 sin^{10}{left (x right )} cos^{11}{left (x right )} + 203490 sin^{8}{left (x right )} cos^{13}{left (x right )} – 54264 sin^{6}{left (x right )} cos^{15}{left (x right )} + 5985 sin^{4}{left (x right )} cos^{17}{left (x right )} – 210 sin^{2}{left (x right )} cos^{19}{left (x right )} + cos^{21}{left (x right )}right)^{2} + 11 left(sin^{21}{left (x right )} – 210 sin^{19}{left (x right )} cos^{2}{left (x right )} + 5985 sin^{17}{left (x right )} cos^{4}{left (x right )} – 54264 sin^{15}{left (x right )} cos^{6}{left (x right )} + 203490 sin^{13}{left (x right )} cos^{8}{left (x right )} – 352716 sin^{11}{left (x right )} cos^{10}{left (x right )} + 293930 sin^{9}{left (x right )} cos^{12}{left (x right )} – 116280 sin^{7}{left (x right )} cos^{14}{left (x right )} + 20349 sin^{5}{left (x right )} cos^{16}{left (x right )} – 1330 sin^{3}{left (x right )} cos^{18}{left (x right )} + 21 sin{left (x right )} cos^{20}{left (x right )}right)^{2}$$
