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Дано

$$frac{54 sin^{2}{left (29 x right )} sin{left (54 x right )}}{29 cos^{2}{left (54 x right )}} + frac{58}{29 cos{left (54 x right )}} cos{left (29 x right )} sin{left (29 x right )}$$
Подстановка условия
$$frac{54 sin^{2}{left (29 x right )} sin{left (54 x right )}}{29 cos^{2}{left (54 x right )}} + frac{58}{29 cos{left (54 x right )}} cos{left (29 x right )} sin{left (29 x right )}$$

((58/(29*cos(54*(1/3))))*cos(29*(1/3)))*sin(29*(1/3)) + ((54*sin(29*(1/3))^2)*sin(54*(1/3)))/(29*cos(54*(1/3))^2)

$$frac{54 sin^{2}{left (29 (1/3) right )} sin{left (54 (1/3) right )}}{29 cos^{2}{left (54 (1/3) right )}} + frac{58}{29 cos{left (54 (1/3) right )}} cos{left (29 (1/3) right )} sin{left (29 (1/3) right )}$$

((58/(29*cos(54/3)))*cos(29/3))*sin(29/3) + ((54*sin(29/3)^2)*sin(54/3))/(29*cos(54/3)^2)

$$frac{54 sin^{2}{left (frac{29}{3} right )} sin{left (frac{54}{3} right )}}{29 cos^{2}{left (frac{54}{3} right )}} + frac{58}{29 cos{left (frac{54}{3} right )}} cos{left (frac{29}{3} right )} sin{left (frac{29}{3} right )}$$

2*cos(29/3)*sin(29/3)/cos(18) + 54*sin(29/3)^2*sin(18)/(29*cos(18)^2)

$$frac{54 sin^{2}{left (frac{29}{3} right )} sin{left (18 right )}}{29 cos^{2}{left (18 right )}} + frac{2 cos{left (frac{29}{3} right )}}{cos{left (18 right )}} sin{left (frac{29}{3} right )}$$
Степени
$$frac{54 sin^{2}{left (29 x right )} sin{left (54 x right )}}{29 cos^{2}{left (54 x right )}} + frac{2 cos{left (29 x right )}}{cos{left (54 x right )}} sin{left (29 x right )}$$
Численный ответ

2.0*cos(29*x)*sin(29*x)/cos(54*x) + 1.86206896551724*sin(29*x)^2*sin(54*x)/cos(54*x)^2

Рациональный знаменатель
$$frac{1}{841 cos^{3}{left (54 x right )}} left(1566 sin^{2}{left (29 x right )} sin{left (54 x right )} cos{left (54 x right )} + 1682 sin{left (29 x right )} cos{left (29 x right )} cos^{2}{left (54 x right )}right)$$
Объединение рациональных выражений
$$frac{2 sin{left (29 x right )}}{29 cos^{2}{left (54 x right )}} left(27 sin{left (29 x right )} sin{left (54 x right )} + 29 cos{left (29 x right )} cos{left (54 x right )}right)$$
Общее упрощение

2*(28*cos(25*x) + cos(83*x))*sin(29*x)
————————————–
2
29*cos (54*x)

$$frac{2 sin{left (29 x right )}}{29 cos^{2}{left (54 x right )}} left(28 cos{left (25 x right )} + cos{left (83 x right )}right)$$
Соберем выражение
$$frac{54}{29} left(- frac{1}{2} cos{left (58 x right )} + frac{1}{2}right) tan{left (54 x right )} sec{left (54 x right )} + sin{left (58 x right )} sec{left (54 x right )}$$
Общий знаменатель

2
54*sin (29*x)*sin(54*x) + 58*cos(29*x)*cos(54*x)*sin(29*x)
———————————————————-
2
29*cos (54*x)

$$frac{1}{29 cos^{2}{left (54 x right )}} left(54 sin^{2}{left (29 x right )} sin{left (54 x right )} + 58 sin{left (29 x right )} cos{left (29 x right )} cos{left (54 x right )}right)$$
Тригонометрическая часть

2*(27*sin(54*x) + 28*sin(4*x) + sin(112*x))
——————————————-
29*(1 + cos(108*x))

$$frac{1}{29 cos{left (108 x right )} + 29} left(56 sin{left (4 x right )} + 54 sin{left (54 x right )} + 2 sin{left (112 x right )}right)$$
Комбинаторика

2*(27*sin(29*x)*sin(54*x) + 29*cos(29*x)*cos(54*x))*sin(29*x)
————————————————————-
2
29*cos (54*x)

$$frac{2 sin{left (29 x right )}}{29 cos^{2}{left (54 x right )}} left(27 sin{left (29 x right )} sin{left (54 x right )} + 29 cos{left (29 x right )} cos{left (54 x right )}right)$$
Раскрыть выражение

2
2*cos(29*x)*sin(29*x) 54*sin (29*x)*sin(54*x)
——————— + ———————–
cos(54*x) 2
29*cos (54*x)

$$frac{54 sin^{2}{left (29 x right )} sin{left (54 x right )}}{29 cos^{2}{left (54 x right )}} + frac{2 cos{left (29 x right )}}{cos{left (54 x right )}} sin{left (29 x right )}$$

2
/ 29 14 15 18 11 10 19 22 7 6 23 26 3 2 27 28 4 25 24 5 8 21 20 9 12 17 16 13 / 29 15 14 11 18 19 10 7 22 23 6 3 26 27 2 28 25 4 5 24 21 8 9 20 17 12 13 16 / 29 14 15 18 11 10 19 22 7 6 23 26 3 2 27 28 4 25 24 5 8 21 20 9 12 17 16 13 / 27 27 23 31 31 23 19 35 35 19 15 39 39 15 11 43 43 11 7 47 47 7 3 51 51 3 53 53 5 49 49 5 9 45 45 9 13 41 41 13 17 37 37 17 21 33 33 21 25 29 29 25
sin (x) – 77558760*cos (x)*sin (x) – 34597290*cos (x)*sin (x) – 20030010*cos (x)*sin (x) – 1560780*cos (x)*sin (x) – 475020*cos (x)*sin (x) – 3654*cos (x)*sin (x) – 406*cos (x)*sin (x) + 29*cos (x)*sin(x) + 23751*cos (x)*sin (x) + 118755*cos (x)*sin (x) + 4292145*cos (x)*sin (x) + 10015005*cos (x)*sin (x) + 51895935*cos (x)*sin (x) + 67863915*cos (x)*sin (x)/*2*cos (x) – 155117520*cos (x)*sin (x) – 69194580*cos (x)*sin (x) – 40060020*cos (x)*sin (x) – 3121560*cos (x)*sin (x) – 950040*cos (x)*sin (x) – 7308*cos (x)*sin (x) – 812*cos (x)*sin (x) + 58*sin (x)*cos(x) + 47502*cos (x)*sin (x) + 237510*cos (x)*sin (x) + 8584290*cos (x)*sin (x) + 20030010*cos (x)*sin (x) + 103791870*cos (x)*sin (x) + 135727830*cos (x)*sin (x)/ 54*sin (x) – 77558760*cos (x)*sin (x) – 34597290*cos (x)*sin (x) – 20030010*cos (x)*sin (x) – 1560780*cos (x)*sin (x) – 475020*cos (x)*sin (x) – 3654*cos (x)*sin (x) – 406*cos (x)*sin (x) + 29*cos (x)*sin(x) + 23751*cos (x)*sin (x) + 118755*cos (x)*sin (x) + 4292145*cos (x)*sin (x) + 10015005*cos (x)*sin (x) + 51895935*cos (x)*sin (x) + 67863915*cos (x)*sin (x)/ * – 1946939425648112*cos (x)*sin (x) – 1085929983159840*cos (x)*sin (x) – 1085929983159840*cos (x)*sin (x) – 183649923622620*cos (x)*sin (x) – 183649923622620*cos (x)*sin (x) – 8654327655120*cos (x)*sin (x) – 8654327655120*cos (x)*sin (x) – 95722852680*cos (x)*sin (x) – 95722852680*cos (x)*sin (x) – 177100560*cos (x)*sin (x) – 177100560*cos (x)*sin (x) – 24804*cos (x)*sin (x) – 24804*cos (x)*sin (x) + 54*cos (x)*sin(x) + 54*sin (x)*cos(x) + 3162510*cos (x)*sin (x) + 3162510*cos (x)*sin (x) + 5317936260*cos (x)*sin (x) + 5317936260*cos (x)*sin (x) + 1108176102180*cos (x)*sin (x) + 1108176102180*cos (x)*sin (x) + 47153358767970*cos (x)*sin (x) + 47153358767970*cos (x)*sin (x) + 520341450264090*cos (x)*sin (x) + 520341450264090*cos (x)*sin (x) + 1683191473897752*cos (x)*sin (x) + 1683191473897752*cos (x)*sin (x)/
————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————- + —————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————
54 54 28 26 24 30 32 22 20 34 36 18 16 38 40 14 12 42 44 10 8 46 48 6 4 50 52 2 2 52 50 4 6 48 46 8 10 44 42 12 14 40 38 16 18 36 34 20 22 32 30 24 26 28 2
cos (x) – sin (x) – 1877405874732108*cos (x)*sin (x) – 1402659561581460*cos (x)*sin (x) – 780512175396135*cos (x)*sin (x) – 321387366339585*cos (x)*sin (x) – 96926348578605*cos (x)*sin (x) – 21094923659355*cos (x)*sin (x) – 3245372870670*cos (x)*sin (x) – 343006888770*cos (x)*sin (x) – 23930713170*cos (x)*sin (x) – 1040465790*cos (x)*sin (x) – 25827165*cos (x)*sin (x) – 316251*cos (x)*sin (x) – 1431*cos (x)*sin (x) + 1431*cos (x)*sin (x) + 316251*cos (x)*sin (x) + 25827165*cos (x)*sin (x) + 1040465790*cos (x)*sin (x) + 23930713170*cos (x)*sin (x) + 343006888770*cos (x)*sin (x) + 3245372870670*cos (x)*sin (x) + 21094923659355*cos (x)*sin (x) + 96926348578605*cos (x)*sin (x) + 321387366339585*cos (x)*sin (x) + 780512175396135*cos (x)*sin (x) + 1402659561581460*cos (x)*sin (x) + 1877405874732108*cos (x)*sin (x) / 54 54 28 26 24 30 32 22 20 34 36 18 16 38 40 14 12 42 44 10 8 46 48 6 4 50 52 2 2 52 50 4 6 48 46 8 10 44 42 12 14 40 38 16 18 36 34 20 22 32 30 24 26 28
29*cos (x) – sin (x) – 1877405874732108*cos (x)*sin (x) – 1402659561581460*cos (x)*sin (x) – 780512175396135*cos (x)*sin (x) – 321387366339585*cos (x)*sin (x) – 96926348578605*cos (x)*sin (x) – 21094923659355*cos (x)*sin (x) – 3245372870670*cos (x)*sin (x) – 343006888770*cos (x)*sin (x) – 23930713170*cos (x)*sin (x) – 1040465790*cos (x)*sin (x) – 25827165*cos (x)*sin (x) – 316251*cos (x)*sin (x) – 1431*cos (x)*sin (x) + 1431*cos (x)*sin (x) + 316251*cos (x)*sin (x) + 25827165*cos (x)*sin (x) + 1040465790*cos (x)*sin (x) + 23930713170*cos (x)*sin (x) + 343006888770*cos (x)*sin (x) + 3245372870670*cos (x)*sin (x) + 21094923659355*cos (x)*sin (x) + 96926348578605*cos (x)*sin (x) + 321387366339585*cos (x)*sin (x) + 780512175396135*cos (x)*sin (x) + 1402659561581460*cos (x)*sin (x) + 1877405874732108*cos (x)*sin (x)/

$$frac{left(58 sin^{28}{left (x right )} cos{left (x right )} – 7308 sin^{26}{left (x right )} cos^{3}{left (x right )} + 237510 sin^{24}{left (x right )} cos^{5}{left (x right )} – 3121560 sin^{22}{left (x right )} cos^{7}{left (x right )} + 20030010 sin^{20}{left (x right )} cos^{9}{left (x right )} – 69194580 sin^{18}{left (x right )} cos^{11}{left (x right )} + 135727830 sin^{16}{left (x right )} cos^{13}{left (x right )} – 155117520 sin^{14}{left (x right )} cos^{15}{left (x right )} + 103791870 sin^{12}{left (x right )} cos^{17}{left (x right )} – 40060020 sin^{10}{left (x right )} cos^{19}{left (x right )} + 8584290 sin^{8}{left (x right )} cos^{21}{left (x right )} – 950040 sin^{6}{left (x right )} cos^{23}{left (x right )} + 47502 sin^{4}{left (x right )} cos^{25}{left (x right )} – 812 sin^{2}{left (x right )} cos^{27}{left (x right )} + 2 cos^{29}{left (x right )}right) left(sin^{29}{left (x right )} – 406 sin^{27}{left (x right )} cos^{2}{left (x right )} + 23751 sin^{25}{left (x right )} cos^{4}{left (x right )} – 475020 sin^{23}{left (x right )} cos^{6}{left (x right )} + 4292145 sin^{21}{left (x right )} cos^{8}{left (x right )} – 20030010 sin^{19}{left (x right )} cos^{10}{left (x right )} + 51895935 sin^{17}{left (x right )} cos^{12}{left (x right )} – 77558760 sin^{15}{left (x right )} cos^{14}{left (x right )} + 67863915 sin^{13}{left (x right )} cos^{16}{left (x right )} – 34597290 sin^{11}{left (x right )} cos^{18}{left (x right )} + 10015005 sin^{9}{left (x right )} cos^{20}{left (x right )} – 1560780 sin^{7}{left (x right )} cos^{22}{left (x right )} + 118755 sin^{5}{left (x right )} cos^{24}{left (x right )} – 3654 sin^{3}{left (x right )} cos^{26}{left (x right )} + 29 sin{left (x right )} cos^{28}{left (x right )}right)}{- sin^{54}{left (x right )} + 1431 sin^{52}{left (x right )} cos^{2}{left (x right )} – 316251 sin^{50}{left (x right )} cos^{4}{left (x right )} + 25827165 sin^{48}{left (x right )} cos^{6}{left (x right )} – 1040465790 sin^{46}{left (x right )} cos^{8}{left (x right )} + 23930713170 sin^{44}{left (x right )} cos^{10}{left (x right )} – 343006888770 sin^{42}{left (x right )} cos^{12}{left (x right )} + 3245372870670 sin^{40}{left (x right )} cos^{14}{left (x right )} – 21094923659355 sin^{38}{left (x right )} cos^{16}{left (x right )} + 96926348578605 sin^{36}{left (x right )} cos^{18}{left (x right )} – 321387366339585 sin^{34}{left (x right )} cos^{20}{left (x right )} + 780512175396135 sin^{32}{left (x right )} cos^{22}{left (x right )} – 1402659561581460 sin^{30}{left (x right )} cos^{24}{left (x right )} + 1877405874732108 sin^{28}{left (x right )} cos^{26}{left (x right )} – 1877405874732108 sin^{26}{left (x right )} cos^{28}{left (x right )} + 1402659561581460 sin^{24}{left (x right )} cos^{30}{left (x right )} – 780512175396135 sin^{22}{left (x right )} cos^{32}{left (x right )} + 321387366339585 sin^{20}{left (x right )} cos^{34}{left (x right )} – 96926348578605 sin^{18}{left (x right )} cos^{36}{left (x right )} + 21094923659355 sin^{16}{left (x right )} cos^{38}{left (x right )} – 3245372870670 sin^{14}{left (x right )} cos^{40}{left (x right )} + 343006888770 sin^{12}{left (x right )} cos^{42}{left (x right )} – 23930713170 sin^{10}{left (x right )} cos^{44}{left (x right )} + 1040465790 sin^{8}{left (x right )} cos^{46}{left (x right )} – 25827165 sin^{6}{left (x right )} cos^{48}{left (x right )} + 316251 sin^{4}{left (x right )} cos^{50}{left (x right )} – 1431 sin^{2}{left (x right )} cos^{52}{left (x right )} + cos^{54}{left (x right )}} + frac{54 left(sin^{29}{left (x right )} – 406 sin^{27}{left (x right )} cos^{2}{left (x right )} + 23751 sin^{25}{left (x right )} cos^{4}{left (x right )} – 475020 sin^{23}{left (x right )} cos^{6}{left (x right )} + 4292145 sin^{21}{left (x right )} cos^{8}{left (x right )} – 20030010 sin^{19}{left (x right )} cos^{10}{left (x right )} + 51895935 sin^{17}{left (x right )} cos^{12}{left (x right )} – 77558760 sin^{15}{left (x right )} cos^{14}{left (x right )} + 67863915 sin^{13}{left (x right )} cos^{16}{left (x right )} – 34597290 sin^{11}{left (x right )} cos^{18}{left (x right )} + 10015005 sin^{9}{left (x right )} cos^{20}{left (x right )} – 1560780 sin^{7}{left (x right )} cos^{22}{left (x right )} + 118755 sin^{5}{left (x right )} cos^{24}{left (x right )} – 3654 sin^{3}{left (x right )} cos^{26}{left (x right )} + 29 sin{left (x right )} cos^{28}{left (x right )}right)^{2} left(54 sin^{53}{left (x right )} cos{left (x right )} – 24804 sin^{51}{left (x right )} cos^{3}{left (x right )} + 3162510 sin^{49}{left (x right )} cos^{5}{left (x right )} – 177100560 sin^{47}{left (x right )} cos^{7}{left (x right )} + 5317936260 sin^{45}{left (x right )} cos^{9}{left (x right )} – 95722852680 sin^{43}{left (x right )} cos^{11}{left (x right )} + 1108176102180 sin^{41}{left (x right )} cos^{13}{left (x right )} – 8654327655120 sin^{39}{left (x right )} cos^{15}{left (x right )} + 47153358767970 sin^{37}{left (x right )} cos^{17}{left (x right )} – 183649923622620 sin^{35}{left (x right )} cos^{19}{left (x right )} + 520341450264090 sin^{33}{left (x right )} cos^{21}{left (x right )} – 1085929983159840 sin^{31}{left (x right )} cos^{23}{left (x right )} + 1683191473897752 sin^{29}{left (x right )} cos^{25}{left (x right )} – 1946939425648112 sin^{27}{left (x right )} cos^{27}{left (x right )} + 1683191473897752 sin^{25}{left (x right )} cos^{29}{left (x right )} – 1085929983159840 sin^{23}{left (x right )} cos^{31}{left (x right )} + 520341450264090 sin^{21}{left (x right )} cos^{33}{left (x right )} – 183649923622620 sin^{19}{left (x right )} cos^{35}{left (x right )} + 47153358767970 sin^{17}{left (x right )} cos^{37}{left (x right )} – 8654327655120 sin^{15}{left (x right )} cos^{39}{left (x right )} + 1108176102180 sin^{13}{left (x right )} cos^{41}{left (x right )} – 95722852680 sin^{11}{left (x right )} cos^{43}{left (x right )} + 5317936260 sin^{9}{left (x right )} cos^{45}{left (x right )} – 177100560 sin^{7}{left (x right )} cos^{47}{left (x right )} + 3162510 sin^{5}{left (x right )} cos^{49}{left (x right )} – 24804 sin^{3}{left (x right )} cos^{51}{left (x right )} + 54 sin{left (x right )} cos^{53}{left (x right )}right)}{29 left(- sin^{54}{left (x right )} + 1431 sin^{52}{left (x right )} cos^{2}{left (x right )} – 316251 sin^{50}{left (x right )} cos^{4}{left (x right )} + 25827165 sin^{48}{left (x right )} cos^{6}{left (x right )} – 1040465790 sin^{46}{left (x right )} cos^{8}{left (x right )} + 23930713170 sin^{44}{left (x right )} cos^{10}{left (x right )} – 343006888770 sin^{42}{left (x right )} cos^{12}{left (x right )} + 3245372870670 sin^{40}{left (x right )} cos^{14}{left (x right )} – 21094923659355 sin^{38}{left (x right )} cos^{16}{left (x right )} + 96926348578605 sin^{36}{left (x right )} cos^{18}{left (x right )} – 321387366339585 sin^{34}{left (x right )} cos^{20}{left (x right )} + 780512175396135 sin^{32}{left (x right )} cos^{22}{left (x right )} – 1402659561581460 sin^{30}{left (x right )} cos^{24}{left (x right )} + 1877405874732108 sin^{28}{left (x right )} cos^{26}{left (x right )} – 1877405874732108 sin^{26}{left (x right )} cos^{28}{left (x right )} + 1402659561581460 sin^{24}{left (x right )} cos^{30}{left (x right )} – 780512175396135 sin^{22}{left (x right )} cos^{32}{left (x right )} + 321387366339585 sin^{20}{left (x right )} cos^{34}{left (x right )} – 96926348578605 sin^{18}{left (
x right )} cos^{36}{left (x right )} + 21094923659355 sin^{16}{left (x right )} cos^{38}{left (x right )} – 3245372870670 sin^{14}{left (x right )} cos^{40}{left (x right )} + 343006888770 sin^{12}{left (x right )} cos^{42}{left (x right )} – 23930713170 sin^{10}{left (x right )} cos^{44}{left (x right )} + 1040465790 sin^{8}{left (x right )} cos^{46}{left (x right )} – 25827165 sin^{6}{left (x right )} cos^{48}{left (x right )} + 316251 sin^{4}{left (x right )} cos^{50}{left (x right )} – 1431 sin^{2}{left (x right )} cos^{52}{left (x right )} + cos^{54}{left (x right )}right)^{2}}$$
   
4.02
yaraya
Кандидат искусствоведения, педагог с большим практическим опытом работы и значительным опытом написания различных видов работ (дипломные, курсовые, статьи, контрольный, рефераты). - Каждая работа как ребенок... Рождаю, холю, лелею...-