Дано
$$frac{38}{19 cos{left (38 x right )}} cos{left (19 x right )} sin{left (19 x right )} tan{left (log{left (2 right )} right )} + frac{tan{left (log{left (2 right )} right )}}{cos^{2}{left (38 x right )}} 2 sin^{2}{left (19 x right )} sin{left (38 x right )}$$
Подстановка условия
$$frac{38}{19 cos{left (38 x right )}} cos{left (19 x right )} sin{left (19 x right )} tan{left (log{left (2 right )} right )} + frac{tan{left (log{left (2 right )} right )}}{cos^{2}{left (38 x right )}} 2 sin^{2}{left (19 x right )} sin{left (38 x right )}$$
(((2*sin(19*(1/4))^2)*sin(38*(1/4)))*tan(log(2)))/cos(38*(1/4))^2 + (((38/(19*cos(38*(1/4))))*cos(19*(1/4)))*sin(19*(1/4)))*tan(log(2))
$$frac{38}{19 cos{left (38 (1/4) right )}} cos{left (19 (1/4) right )} sin{left (19 (1/4) right )} tan{left (log{left (2 right )} right )} + frac{tan{left (log{left (2 right )} right )}}{cos^{2}{left (38 (1/4) right )}} 2 sin^{2}{left (19 (1/4) right )} sin{left (38 (1/4) right )}$$
(((2*sin(19/4)^2)*sin(38/4))*tan(log(2)))/cos(38/4)^2 + (((38/(19*cos(38/4)))*cos(19/4))*sin(19/4))*tan(log(2))
$$frac{tan{left (log{left (2 right )} right )}}{cos^{2}{left (frac{38}{4} right )}} 2 sin^{2}{left (frac{19}{4} right )} sin{left (frac{38}{4} right )} + frac{38}{19 cos{left (frac{38}{4} right )}} cos{left (frac{19}{4} right )} sin{left (frac{19}{4} right )} tan{left (log{left (2 right )} right )}$$
2*cos(19/4)*sin(19/4)*tan(log(2))/cos(19/2) + 2*sin(19/4)^2*sin(19/2)*tan(log(2))/cos(19/2)^2
$$frac{2 sin^{2}{left (frac{19}{4} right )}}{cos^{2}{left (frac{19}{2} right )}} sin{left (frac{19}{2} right )} tan{left (log{left (2 right )} right )} + frac{2 cos{left (frac{19}{4} right )}}{cos{left (frac{19}{2} right )}} sin{left (frac{19}{4} right )} tan{left (log{left (2 right )} right )}$$
Степени
$$frac{2 sin^{2}{left (19 x right )}}{cos^{2}{left (38 x right )}} sin{left (38 x right )} tan{left (log{left (2 right )} right )} + frac{2 cos{left (19 x right )}}{cos{left (38 x right )}} sin{left (19 x right )} tan{left (log{left (2 right )} right )}$$
Численный ответ
1.66128175572157*cos(19*x)*sin(19*x)/cos(38*x) + 1.66128175572157*sin(19*x)^2*sin(38*x)/cos(38*x)^2
Рациональный знаменатель
$$frac{1}{19 cos^{3}{left (38 x right )}} left(38 sin^{2}{left (19 x right )} sin{left (38 x right )} cos{left (38 x right )} tan{left (log{left (2 right )} right )} + 38 sin{left (19 x right )} cos{left (19 x right )} cos^{2}{left (38 x right )} tan{left (log{left (2 right )} right )}right)$$
Объединение рациональных выражений
$$frac{2 sin{left (19 x right )}}{cos^{2}{left (38 x right )}} left(sin{left (19 x right )} sin{left (38 x right )} + cos{left (19 x right )} cos{left (38 x right )}right) tan{left (log{left (2 right )} right )}$$
Общее упрощение
2*sin(38*x)*tan(log(2))
———————–
1 + cos(76*x)
$$frac{2 sin{left (38 x right )} tan{left (log{left (2 right )} right )}}{cos{left (76 x right )} + 1}$$
Соберем выражение
$$frac{1}{cos^{2}{left (38 x right )}} left(2 sin^{2}{left (19 x right )} sin{left (38 x right )} tan{left (log{left (2 right )} right )} + 2 sin{left (19 x right )} cos{left (19 x right )} cos{left (38 x right )} tan{left (log{left (2 right )} right )}right)$$
/1 cos(38*x)
tan(38*x)*tan(log(2)) + 2*|- – ———|*sec(38*x)*tan(38*x)*tan(log(2))
2 2 /
$$2 left(- frac{1}{2} cos{left (38 x right )} + frac{1}{2}right) tan{left (38 x right )} tan{left (log{left (2 right )} right )} sec{left (38 x right )} + tan{left (38 x right )} tan{left (log{left (2 right )} right )}$$
Общий знаменатель
2
2*sin (19*x)*sin(38*x)*tan(log(2)) + 2*cos(19*x)*cos(38*x)*sin(19*x)*tan(log(2))
——————————————————————————–
2
cos (38*x)
$$frac{1}{cos^{2}{left (38 x right )}} left(2 sin^{2}{left (19 x right )} sin{left (38 x right )} tan{left (log{left (2 right )} right )} + 2 sin{left (19 x right )} cos{left (19 x right )} cos{left (38 x right )} tan{left (log{left (2 right )} right )}right)$$
Тригонометрическая часть
2*sin(38*x)*tan(log(2))
———————–
1 + cos(76*x)
$$frac{2 sin{left (38 x right )} tan{left (log{left (2 right )} right )}}{cos{left (76 x right )} + 1}$$
Комбинаторика
2*(cos(19*x)*cos(38*x) + sin(19*x)*sin(38*x))*sin(19*x)*tan(log(2))
——————————————————————-
2
cos (38*x)
$$frac{2 sin{left (19 x right )}}{cos^{2}{left (38 x right )}} left(sin{left (19 x right )} sin{left (38 x right )} + cos{left (19 x right )} cos{left (38 x right )}right) tan{left (log{left (2 right )} right )}$$
Раскрыть выражение
2
/ 19 8 11 12 7 4 15 16 3 18 2 17 14 5 6 13 10 9 / 19 19 15 23 23 15 11 27 27 11 7 31 31 7 3 35 35 3 37 37 5 33 33 5 9 29 29 9 13 25 25 13 17 21 21 17 / 19 9 10 13 6 5 14 17 2 18 3 16 15 4 7 12 11 8 / 19 8 11 12 7 4 15 16 3 18 2 17 14 5 6 13 10 9
2* – sin (x) – 75582*cos (x)*sin (x) – 50388*cos (x)*sin (x) – 3876*cos (x)*sin (x) – 969*cos (x)*sin (x) + 19*cos (x)*sin(x) + 171*cos (x)*sin (x) + 11628*cos (x)*sin (x) + 27132*cos (x)*sin (x) + 92378*cos (x)*sin (x)/ * – 35345263800*cos (x)*sin (x) – 15471286560*cos (x)*sin (x) – 15471286560*cos (x)*sin (x) – 1203322288*cos (x)*sin (x) – 1203322288*cos (x)*sin (x) – 12620256*cos (x)*sin (x) – 12620256*cos (x)*sin (x) – 8436*cos (x)*sin (x) – 8436*cos (x)*sin (x) + 38*cos (x)*sin(x) + 38*sin (x)*cos(x) + 501942*cos (x)*sin (x) + 501942*cos (x)*sin (x) + 163011640*cos (x)*sin (x) + 163011640*cos (x)*sin (x) + 5414950296*cos (x)*sin (x) + 5414950296*cos (x)*sin (x) + 28781143380*cos (x)*sin (x) + 28781143380*cos (x)*sin (x)/*tan(log(2)) 2*cos (x) – 92378*cos (x)*sin (x) – 27132*cos (x)*sin (x) – 11628*cos (x)*sin (x) – 171*cos (x)*sin (x) – 19*sin (x)*cos(x) + 969*cos (x)*sin (x) + 3876*cos (x)*sin (x) + 50388*cos (x)*sin (x) + 75582*cos (x)*sin (x)/* – sin (x) – 75582*cos (x)*sin (x) – 50388*cos (x)*sin (x) – 3876*cos (x)*sin (x) – 969*cos (x)*sin (x) + 19*cos (x)*sin(x) + 171*cos (x)*sin (x) + 11628*cos (x)*sin (x) + 27132*cos (x)*sin (x) + 92378*cos (x)*sin (x)/*tan(log(2))
—————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————– + ———————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————
2 38 38 20 18 16 22 24 14 12 26 28 10 8 30 32 6 4 34 36 2 2 36 34 4 6 32 30 8 10 28 26 12 14 24 22 16 18 20
/ 38 38 20 18 16 22 24 14 12 26 28 10 8 30 32 6 4 34 36 2 2 36 34 4 6 32 30 8 10 28 26 12 14 24 22 16 18 20 cos (x) – sin (x) – 33578000610*cos (x)*sin (x) – 22239974430*cos (x)*sin (x) – 9669554100*cos (x)*sin (x) – 2707475148*cos (x)*sin (x) – 472733756*cos (x)*sin (x) – 48903492*cos (x)*sin (x) – 2760681*cos (x)*sin (x) – 73815*cos (x)*sin (x) – 703*cos (x)*sin (x) + 703*cos (x)*sin (x) + 73815*cos (x)*sin (x) + 2760681*cos (x)*sin (x) + 48903492*cos (x)*sin (x) + 472733756*cos (x)*sin (x) + 2707475148*cos (x)*sin (x) + 9669554100*cos (x)*sin (x) + 22239974430*cos (x)*sin (x) + 33578000610*cos (x)*sin (x)
cos (x) – sin (x) – 33578000610*cos (x)*sin (x) – 22239974430*cos (x)*sin (x) – 9669554100*cos (x)*sin (x) – 2707475148*cos (x)*sin (x) – 472733756*cos (x)*sin (x) – 48903492*cos (x)*sin (x) – 2760681*cos (x)*sin (x) – 73815*cos (x)*sin (x) – 703*cos (x)*sin (x) + 703*cos (x)*sin (x) + 73815*cos (x)*sin (x) + 2760681*cos (x)*sin (x) + 48903492*cos (x)*sin (x) + 472733756*cos (x)*sin (x) + 2707475148*cos (x)*sin (x) + 9669554100*cos (x)*sin (x) + 22239974430*cos (x)*sin (x) + 33578000610*cos (x)*sin (x)/
$$frac{2 left(- 19 sin^{18}{left (x right )} cos{left (x right )} + 969 sin^{16}{left (x right )} cos^{3}{left (x right )} – 11628 sin^{14}{left (x right )} cos^{5}{left (x right )} + 50388 sin^{12}{left (x right )} cos^{7}{left (x right )} – 92378 sin^{10}{left (x right )} cos^{9}{left (x right )} + 75582 sin^{8}{left (x right )} cos^{11}{left (x right )} – 27132 sin^{6}{left (x right )} cos^{13}{left (x right )} + 3876 sin^{4}{left (x right )} cos^{15}{left (x right )} – 171 sin^{2}{left (x right )} cos^{17}{left (x right )} + cos^{19}{left (x right )}right) left(- sin^{19}{left (x right )} + 171 sin^{17}{left (x right )} cos^{2}{left (x right )} – 3876 sin^{15}{left (x right )} cos^{4}{left (x right )} + 27132 sin^{13}{left (x right )} cos^{6}{left (x right )} – 75582 sin^{11}{left (x right )} cos^{8}{left (x right )} + 92378 sin^{9}{left (x right )} cos^{10}{left (x right )} – 50388 sin^{7}{left (x right )} cos^{12}{left (x right )} + 11628 sin^{5}{left (x right )} cos^{14}{left (x right )} – 969 sin^{3}{left (x right )} cos^{16}{left (x right )} + 19 sin{left (x right )} cos^{18}{left (x right )}right) tan{left (log{left (2 right )} right )}}{- sin^{38}{left (x right )} + 703 sin^{36}{left (x right )} cos^{2}{left (x right )} – 73815 sin^{34}{left (x right )} cos^{4}{left (x right )} + 2760681 sin^{32}{left (x right )} cos^{6}{left (x right )} – 48903492 sin^{30}{left (x right )} cos^{8}{left (x right )} + 472733756 sin^{28}{left (x right )} cos^{10}{left (x right )} – 2707475148 sin^{26}{left (x right )} cos^{12}{left (x right )} + 9669554100 sin^{24}{left (x right )} cos^{14}{left (x right )} – 22239974430 sin^{22}{left (x right )} cos^{16}{left (x right )} + 33578000610 sin^{20}{left (x right )} cos^{18}{left (x right )} – 33578000610 sin^{18}{left (x right )} cos^{20}{left (x right )} + 22239974430 sin^{16}{left (x right )} cos^{22}{left (x right )} – 9669554100 sin^{14}{left (x right )} cos^{24}{left (x right )} + 2707475148 sin^{12}{left (x right )} cos^{26}{left (x right )} – 472733756 sin^{10}{left (x right )} cos^{28}{left (x right )} + 48903492 sin^{8}{left (x right )} cos^{30}{left (x right )} – 2760681 sin^{6}{left (x right )} cos^{32}{left (x right )} + 73815 sin^{4}{left (x right )} cos^{34}{left (x right )} – 703 sin^{2}{left (x right )} cos^{36}{left (x right )} + cos^{38}{left (x right )}} + frac{2 left(- sin^{19}{left (x right )} + 171 sin^{17}{left (x right )} cos^{2}{left (x right )} – 3876 sin^{15}{left (x right )} cos^{4}{left (x right )} + 27132 sin^{13}{left (x right )} cos^{6}{left (x right )} – 75582 sin^{11}{left (x right )} cos^{8}{left (x right )} + 92378 sin^{9}{left (x right )} cos^{10}{left (x right )} – 50388 sin^{7}{left (x right )} cos^{12}{left (x right )} + 11628 sin^{5}{left (x right )} cos^{14}{left (x right )} – 969 sin^{3}{left (x right )} cos^{16}{left (x right )} + 19 sin{left (x right )} cos^{18}{left (x right )}right)^{2} left(38 sin^{37}{left (x right )} cos{left (x right )} – 8436 sin^{35}{left (x right )} cos^{3}{left (x right )} + 501942 sin^{33}{left (x right )} cos^{5}{left (x right )} – 12620256 sin^{31}{left (x right )} cos^{7}{left (x right )} + 163011640 sin^{29}{left (x right )} cos^{9}{left (x right )} – 1203322288 sin^{27}{left (x right )} cos^{11}{left (x right )} + 5414950296 sin^{25}{left (x right )} cos^{13}{left (x right )} – 15471286560 sin^{23}{left (x right )} cos^{15}{left (x right )} + 28781143380 sin^{21}{left (x right )} cos^{17}{left (x right )} – 35345263800 sin^{19}{left (x right )} cos^{19}{left (x right )} + 28781143380 sin^{17}{left (x right )} cos^{21}{left (x right )} – 15471286560 sin^{15}{left (x right )} cos^{23}{left (x right )} + 5414950296 sin^{13}{left (x right )} cos^{25}{left (x right )} – 1203322288 sin^{11}{left (x right )} cos^{27}{left (x right )} + 163011640 sin^{9}{left (x right )} cos^{29}{left (x right )} – 12620256 sin^{7}{left (x right )} cos^{31}{left (x right )} + 501942 sin^{5}{left (x right )} cos^{33}{left (x right )} – 8436 sin^{3}{left (x right )} cos^{35}{left (x right )} + 38 sin{left (x right )} cos^{37}{left (x right )}right) tan{left (log{left (2 right )} right )}}{left(- sin^{38}{left (x right )} + 703 sin^{36}{left (x right )} cos^{2}{left (x right )} – 73815 sin^{34}{left (x right )} cos^{4}{left (x right )} + 2760681 sin^{32}{left (x right )} cos^{6}{left (x right )} – 48903492 sin^{30}{left (x right )} cos^{8}{left (x right )} + 472733756 sin^{28}{left (x right )} cos^{10}{left (x right )} – 2707475148 sin^{26}{left (x right )} cos^{12}{left (x right )} + 9669554100 sin^{24}{left (x right )} cos^{14}{left (x right )} – 22239974430 sin^{22}{left (x right )} cos^{16}{left (x right )} + 33578000610 sin^{20}{left (x right )} cos^{18}{left (x right )} – 33578000610 sin^{18}{left (x right )} cos^{20}{left (x right )} + 22239974430 sin^{16}{left (x right )} cos^{22}{left (x right )} – 9669554100 sin^{14}{left (x right )} cos^{24}{left (x right )} + 2707475148 sin^{12}{left (x right )} cos^{26}{left (x right )} – 472733756 sin^{10}{left (x right )} cos^{28}{left (x right )} + 48903492 sin^{8}{left (x right )} cos^{30}{left (x right )} – 2760681 sin^{6}{left (x right )} cos^{32}{left (x right )} + 73815 sin^{4}{left (x right )} cos^{34}{left (x right )} – 703 sin^{2}{left (x right )} cos^{36}{left (x right )} + cos^{38}{left (x right )}right)^{2}}$$
2
2*sin (19*x)*sin(38*x)*tan(log(2)) 2*cos(19*x)*sin(19*x)*tan(log(2))
———————————- + ———————————
2 cos(38*x)
cos (38*x)
$$frac{tan{left (log{left (2 right )} right )}}{cos^{2}{left (38 x right )}} 2 sin^{2}{left (19 x right )} sin{left (38 x right )} + frac{2 cos{left (19 x right )}}{cos{left (38 x right )}} sin{left (19 x right )} tan{left (log{left (2 right )} right )}$$
2
2*cos(19*x)*sin(19*x)*tan(log(2)) 2*sin (19*x)*sin(38*x)*tan(log(2))
——————————— + ———————————-
cos(38*x) 2
cos (38*x)
$$frac{2 sin^{2}{left (19 x right )}}{cos^{2}{left (38 x right )}} sin{left (38 x right )} tan{left (log{left (2 right )} right )} + frac{2 cos{left (19 x right )}}{cos{left (38 x right )}} sin{left (19 x right )} tan{left (log{left (2 right )} right )}$$
