Дано
$$left(tan^{2}{left (36 x right )} + 3 – 2 tan{left (36 x right )}right) 2 cos{left (36 x right )} + – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Подстановка условия
$$left(tan^{2}{left (36 x right )} + 3 – 2 tan{left (36 x right )}right) 2 cos{left (36 x right )} + – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
-3*cos(36*(1/4)) + cos(72*(1/4)) + (2*cos(36*(1/4)))*(3 + tan(36*(1/4))^2 – 2*tan(36*(1/4)))
$$left(tan^{2}{left (36 (1/4) right )} + 3 – 2 tan{left (36 (1/4) right )}right) 2 cos{left (36 (1/4) right )} + – 3 cos{left (36 (1/4) right )} + cos{left (72 (1/4) right )}$$
-3*cos(36/4) + cos(72/4) + (2*cos(36/4))*(3 + tan(36/4)^2 – 2*tan(36/4))
$$left(- 2 tan{left (frac{36}{4} right )} + tan^{2}{left (frac{36}{4} right )} + 3right) 2 cos{left (frac{36}{4} right )} + cos{left (frac{72}{4} right )} – 3 cos{left (frac{36}{4} right )}$$
-3*cos(9) + 2*(3 + tan(9)^2 – 2*tan(9))*cos(9) + cos(18)
$$2 left(tan^{2}{left (9 right )} – 2 tan{left (9 right )} + 3right) cos{left (9 right )} + cos{left (18 right )} – 3 cos{left (9 right )}$$
Степени
$$2 left(tan^{2}{left (36 x right )} – 2 tan{left (36 x right )} + 3right) cos{left (36 x right )} – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Численный ответ
-3.0*cos(36*x) + 2.0*(3.0 + tan(36*x)^2 – 2.0*tan(36*x))*cos(36*x) + cos(72*x)
Рациональный знаменатель
$$2 left(tan^{2}{left (36 x right )} – 2 tan{left (36 x right )} + 3right) cos{left (36 x right )} – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Объединение рациональных выражений
$$2 left(tan^{2}{left (36 x right )} – 2 tan{left (36 x right )} + 3right) cos{left (36 x right )} – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Общее упрощение
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-3*cos(36*x) + 2*3 + tan (36*x) – 2*tan(36*x)/*cos(36*x) + cos(72*x)
$$2 left(tan^{2}{left (36 x right )} – 2 tan{left (36 x right )} + 3right) cos{left (36 x right )} – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Соберем выражение
$$2 sin{left (36 x right )} tan{left (36 x right )} – 4 sin{left (36 x right )} + 3 cos{left (36 x right )} + cos{left (72 x right )}$$
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-3*cos(36*x) + 2*cos(36*x)*3 + tan (36*x) – 2*tan(36*x)/ + cos(72*x)
$$left(tan^{2}{left (36 x right )} + 3 – 2 tan{left (36 x right )}right) 2 cos{left (36 x right )} – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Общий знаменатель
2
3*cos(36*x) – 4*cos(36*x)*tan(36*x) + 2*tan (36*x)*cos(36*x) + cos(72*x)
$$2 cos{left (36 x right )} tan^{2}{left (36 x right )} – 4 cos{left (36 x right )} tan{left (36 x right )} + 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Комбинаторика
2
3*cos(36*x) – 4*cos(36*x)*tan(36*x) + 2*tan (36*x)*cos(36*x) + cos(72*x)
$$2 cos{left (36 x right )} tan^{2}{left (36 x right )} – 4 cos{left (36 x right )} tan{left (36 x right )} + 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Тригонометрическая часть
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-3*cos(36*x) + 2*3 + tan (36*x) – 2*tan(36*x)/*cos(36*x) + cos(72*x)
$$2 left(tan^{2}{left (36 x right )} – 2 tan{left (36 x right )} + 3right) cos{left (36 x right )} – 3 cos{left (36 x right )} + cos{left (72 x right )}$$
Раскрыть выражение
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| / 19 15 23 11 27 7 31 3 35 33 5 29 9 25 13 21 17 17 21 13 25 9 29 5 33 35 3 31 7 27 11 23 15 19 |
72 72 36 36 | – 8597496600*tan (x) – 5567902560*tan (x) – 2310789600*tan (x) – 600805296*tan (x) – 94143280*tan (x) – 8347680*tan (x) – 376992*tan (x) – 7140*tan (x) – 36*tan (x) + 36*tan(x) + 7140*tan (x) + 376992*tan (x) + 8347680*tan (x) + 94143280*tan (x) + 600805296*tan (x) + 2310789600*tan (x) + 5567902560*tan (x) + 8597496600*tan (x)/ – 17194993200*tan (x) – 11135805120*tan (x) – 4621579200*tan (x) – 1201610592*tan (x) – 188286560*tan (x) – 16695360*tan (x) – 753984*tan (x) – 14280*tan (x) – 72*tan(x) + 72*tan (x) + 14280*tan (x) + 753984*tan (x) + 16695360*tan (x) + 188286560*tan (x) + 1201610592*tan (x) + 4621579200*tan (x) + 11135805120*tan (x) + 17194993200*tan (x)| / 36 36 18 18 14 22 22 14 10 26 26 10 6 30 30 6 2 34 34 2 4 32 32 4 8 28 28 8 12 24 24 12 16 20 20 16 34 38 38 34 30 42 42 30 26 46 46 26 22 50 50 22 18 54 54 18 14 58 58 14 10 62 62 10 16 20 20 16 12 24 24 12 6 66 66 6 8 28 28 8 4 32 32 4 2 70 70 2 2 34 34 2 4 68 68 4 6 30 30 6 10 26 26 10 14 22 22 14 8 64 64 8 18 18 12 60 60 12 16 56 56 16 20 52 52 20 24 48 48 24 28 44 44 28 32 40 40 32 36 36
cos (x) + sin (x) – 3*cos (x) – 3*sin (x) + |3 + ————————————————————————————————————————————————————————————————————————————————————————————————————————————————————- + —————————————————————————————————————————————————————————————————————————————————————————————————————————————————————–|*2*cos (x) + 2*sin (x) – 18150270600*cos (x)*sin (x) – 7592594400*cos (x)*sin (x) – 7592594400*cos (x)*sin (x) – 508373712*cos (x)*sin (x) – 508373712*cos (x)*sin (x) – 3895584*cos (x)*sin (x) – 3895584*cos (x)*sin (x) – 1260*cos (x)*sin (x) – 1260*cos (x)*sin (x) + 117810*cos (x)*sin (x) + 117810*cos (x)*sin (x) + 60520680*cos (x)*sin (x) + 60520680*cos (x)*sin (x) + 2503355400*cos (x)*sin (x) + 2503355400*cos (x)*sin (x) + 14615744220*cos (x)*sin (x) + 14615744220*cos (x)*sin (x)/ – 396561735952215036840*cos (x)*sin (x) – 396561735952215036840*cos (x)*sin (x) – 164307576757973059488*cos (x)*sin (x) – 164307576757973059488*cos (x)*sin (x) – 27593523553342842144*cos (x)*sin (x) – 27593523553342842144*cos (x)*sin (x) – 1791242627540058576*cos (x)*sin (x) – 1791242627540058576*cos (x)*sin (x) – 41432089765583440*cos (x)*sin (x) – 41432089765583440*cos (x)*sin (x) – 298824321028320*cos (x)*sin (x) – 298824321028320*cos (x)*sin (x) – 536211932256*cos (x)*sin (x) – 536211932256*cos (x)*sin (x) – 21923616330*cos (x)*sin (x) – 21923616330*cos (x)*sin (x) – 3755033100*cos (x)*sin (x) – 3755033100*cos (x)*sin (x) – 156238908*cos (x)*sin (x) – 156238908*cos (x)*sin (x) – 90781020*cos (x)*sin (x) – 90781020*cos (x)*sin (x) – 176715*cos (x)*sin (x) – 176715*cos (x)*sin (x) – 2556*cos (x)*sin (x) – 2556*cos (x)*sin (x) + 1890*cos (x)*sin (x) + 1890*cos (x)*sin (x) + 1028790*cos (x)*sin (x) + 1028790*cos (x)*sin (x) + 5843376*cos (x)*sin (x) + 5843376*cos (x)*sin (x) + 762560568*cos (x)*sin (x) + 762560568*cos (x)*sin (x) + 11388891600*cos (x)*sin (x) + 11388891600*cos (x)*sin (x) + 11969016345*cos (x)*sin (x) + 11969016345*cos (x)*sin (x) + 27225405900*cos (x)*sin (x) + 15363284301456*cos (x)*sin (x) + 15363284301456*cos (x)*sin (x) + 4116305022165108*cos (x)*sin (x) + 4116305022165108*cos (x)*sin (x) + 312049055023946856*cos (x)*sin (x) + 312049055023946856*cos (x)*sin (x) + 7950261662089028100*cos (x)*sin (x) + 7950261662089028100*cos (x)*sin (x) + 75553695443676829680*cos (x)*sin (x) + 75553695443676829680*cos (x)*sin (x) + 285219402396400814958*cos (x)*sin (x) + 285219402396400814958*cos (x)*sin (x) + 442512540276836779204*cos (x)*sin (x)
| 2 36 18 14 22 10 26 6 30 2 34 4 32 8 28 12 24 16 20 |
| / 36 18 14 22 10 26 6 30 2 34 4 32 8 28 12 24 16 20 1 + tan (x) – 9075135300*tan (x) – 3796297200*tan (x) – 3796297200*tan (x) – 254186856*tan (x) – 254186856*tan (x) – 1947792*tan (x) – 1947792*tan (x) – 630*tan (x) – 630*tan (x) + 58905*tan (x) + 58905*tan (x) + 30260340*tan (x) + 30260340*tan (x) + 1251677700*tan (x) + 1251677700*tan (x) + 7307872110*tan (x) + 7307872110*tan (x) |
1 + tan (x) – 9075135300*tan (x) – 3796297200*tan (x) – 3796297200*tan (x) – 254186856*tan (x) – 254186856*tan (x) – 1947792*tan (x) – 1947792*tan (x) – 630*tan (x) – 630*tan (x) + 58905*tan (x) + 58905*tan (x) + 30260340*tan (x) + 30260340*tan (x) + 1251677700*tan (x) + 1251677700*tan (x) + 7307872110*tan (x) + 7307872110*tan (x)/ /
$$left(frac{left(- 36 tan^{35}{left (x right )} + 7140 tan^{33}{left (x right )} – 376992 tan^{31}{left (x right )} + 8347680 tan^{29}{left (x right )} – 94143280 tan^{27}{left (x right )} + 600805296 tan^{25}{left (x right )} – 2310789600 tan^{23}{left (x right )} + 5567902560 tan^{21}{left (x right )} – 8597496600 tan^{19}{left (x right )} + 8597496600 tan^{17}{left (x right )} – 5567902560 tan^{15}{left (x right )} + 2310789600 tan^{13}{left (x right )} – 600805296 tan^{11}{left (x right )} + 94143280 tan^{9}{left (x right )} – 8347680 tan^{7}{left (x right )} + 376992 tan^{5}{left (x right )} – 7140 tan^{3}{left (x right )} + 36 tan{left (x right )}right)^{2}}{left(tan^{36}{left (x right )} – 630 tan^{34}{left (x right )} + 58905 tan^{32}{left (x right )} – 1947792 tan^{30}{left (x right )} + 30260340 tan^{28}{left (x right )} – 254186856 tan^{26}{left (x right )} + 1251677700 tan^{24}{left (x right )} – 3796297200 tan^{22}{left (x right )} + 7307872110 tan^{20}{left (x right )} – 9075135300 tan^{18}{left (x right )} + 7307872110 tan^{16}{left (x right )} – 3796297200 tan^{14}{left (x right )} + 1251677700 tan^{12}{left (x right )} – 254186856 tan^{10}{left (x right )} + 30260340 tan^{8}{left (x right )} – 1947792 tan^{6}{left (x right )} + 58905 tan^{4}{left (x right )} – 630 tan^{2}{left (x right )} + 1right)^{2}} + frac{72 tan^{35}{left (x right )} – 14280 tan^{33}{left (x right )} + 753984 tan^{31}{left (x right )} – 16695360 tan^{29}{left (x right )} + 188286560 tan^{27}{left (x right )} – 1201610592 tan^{25}{left (x right )} + 4621579200 tan^{23}{left (x right )} – 11135805120 tan^{21}{left (x right )} + 17194993200 tan^{19}{left (x right )} – 17194993200 tan^{17}{left (x right )} + 11135805120 tan^{15}{left (x right )} – 4621579200 tan^{13}{left (x right )} + 1201610592 tan^{11}{left (x right )} – 188286560 tan^{9}{left (x right )} + 16695360 tan^{7}{left (x right )} – 753984 tan^{5}{left (x right )} + 14280 tan^{3}{left (x right )} – 72 tan{left (x right )}}{tan^{36}{left (x right )} – 630 tan^{34}{left (x right )} + 58905 tan^{32}{left (x right )} – 1947792 tan^{30}{left (x right )} + 30260340 tan^{28}{left (x right )} – 254186856 tan^{26}{left (x right )} + 1251677700 tan^{24}{left (x right )} – 3796297200 tan^{22}{left (x right )} + 7307872110 tan^{20}{left (x right )} – 9075135300 tan^{18}{left (x right )} + 7307872110 tan^{16}{left (x right )} – 3796297200 tan^{14}{left (x right )} + 1251677700 tan^{12}{left (x right )} – 254186856 tan^{10}{left (x right )} + 30260340 tan^{8}{left (x right )} – 1947792 tan^{6}{left (x right )} + 58905 tan^{4}{left (x right )} – 630 tan^{2}{left (x right )} + 1} + 3right) left(2 sin^{36}{left (x right )} – 1260 sin^{34}{left (x right )} cos^{2}{left (x right )} + 117810 sin^{32}{left (x right )} cos^{4}{left (x right )} – 3895584 sin^{30}{left (x right )} cos^{6}{left (x right )} + 60520680 sin^{28}{left (x right )} cos^{8}{left (x right )} – 508373712 sin^{26}{left (x right )} cos^{10}{left (x right )} + 2503355400 sin^{24}{left (x right )} cos^{12}{left (x right )} – 7592594400 sin^{22}{left (x right )} cos^{14}{left (x right )} + 14615744220 sin^{20}{left (x right )} cos^{16}{left (x right )} – 18150270600 sin^{18}{left (x right )} cos^{18}{left (x right )} + 14615744220 sin^{16}{left (x right )} cos^{20}{left (x right )} – 7592594400 sin^{14}{left (x right )} cos^{22}{left (x right )} + 2503355400 sin^{12}{left (x right )} cos^{24}{left (x right )} – 508373712 sin^{10}{left (x right )} cos^{26}{left (x right )} + 60520680 sin^{8}{left (x right )} cos^{28}{left (x right )} – 3895584 sin^{6}{left (x right )} cos^{30}{left (x right )} + 117810 sin^{4}{left (x right )} cos^{32}{left (x right )} – 1260 sin^{2}{left (x right )} cos^{34}{left (x right )} + 2 cos^{36}{left (x right )}right) + sin^{72}{left (x right )} – 2556 sin^{70}{left (x right )} cos^{2}{left (x right )} + 1028790 sin^{68}{left (x right )} cos^{4}{left (x right )} – 156238908 sin^{66}{left (x right )} cos^{6}{left (x right )} + 11969016345 sin^{64}{left (x right )} cos^{8}{left (x right )} – 536211932256 sin^{62}{left (x right )} cos^{10}{left (x right )} + 15363284301456 sin^{60}{left (x right )} cos^{12}{left (x right )} – 298824321028320 sin^{58}{left (x right )} cos^{14}{left (x right )} + 4116305022165108 sin^{56}{left (x right )} cos^{16}{left (x right )} – 41432089765583440 sin^{54}{left (x right )} cos^{18}{left (x right )} + 312049055023946856 sin^{52}{left (x right )} cos^{20}{left (x right )} – 1791242627540058576 sin^{50}{left (x right )} cos^{22}{left (x right )} + 7950261662089028100 sin^{48}{left (x right )} cos^{24}{left (x right )} – 27593523553342842144 sin^{46}{left (x right )} cos^{26}{left (x right )} + 75553695443676829680 sin^{44}{left (x right )} cos^{28}{left (x right )} – 164307576757973059488 sin^{42}{left (x right )} cos^{30}{left (x right )} + 285219402396400814958 sin^{40}{left (x right )} cos^{32}{left (x right )} – 396561735952215036840 sin^{38}{left (x right )} cos^{34}{left (x right )} + 442512540276836779204 sin^{36}{left (x right )} cos^{36}{left (x right )} – 3 sin^{36}{left (x right )} – 396561735952215036840 sin^{34}{left (x right )} cos^{38}{left (x right )} + 1890 sin^{34}{left (x right )} cos^{2}{left (x right )} + 285219402396400814958 sin^{32}{left (x right )} cos^{40}{left (x right )} – 176715 sin^{32}{left (x right )} cos^{4}{left (x right )} – 164307576757973059488 sin^{30}{left (x right )} cos^{42}{left (x right )} + 5843376 sin^{30}{left (x right )} cos^{6}{left (x right )} + 75553695443676829680 sin^{28}{left (x right )} cos^{44}{left (x right )} – 90781020 sin^{28}{left (x right )} cos^{8}{left (x right )} – 27593523553342842144 sin^{26}{left (x right )} cos^{46}{left (x right )} + 762560568 sin^{26}{left (x right )} cos^{10}{left (x right )} + 7950261662089028100 sin^{24}{left (x right )} cos^{48}{left (x right )} – 3755033100 sin^{24}{left (x right )} cos^{12}{left (x right )} – 1791242627540058576 sin^{22}{left (x right )} cos^{50}{left (x right )} + 11388891600 sin^{22}{left (x right )} cos^{14}{left (x right )} + 312049055023946856 sin^{20}{left (x right )} cos^{52}{left (x right )} – 21923616330 sin^{20}{left (x right )} cos^{16}{left (x right )} – 41432089765583440 sin^{18}{left (x right )} cos^{54}{left (x right )} + 27225405900 sin^{18}{left (x right )} cos^{18}{left (x right )} + 4116305022165108 sin^{16}{left (x right )} cos^{56}{left (x right )} – 21923616330 sin^{16}{left (x right )} cos^{20}{left (x right )} – 298824321028320 sin^{14}{left (x right )} cos^{58}{left (x right )} + 11388891600 sin^{14}{left (x right )} cos^{22}{left (x right )} + 15363284301456 sin^{12}{left (x right )} cos^{60}{left (x right )} – 3755033100 sin^{12}{left (x right )} cos^{24}{left (x right )} – 536211932256 sin^{10}{left (x right )} cos^{62}{left (x right )} + 762560568 sin^{10}{left (x right )} cos^{26}{left (x right )} + 11969016345 sin^{8}{left (x right )} cos^{64}{left (x right )} – 90781020 sin^{8}{left (x right )} cos^{28}{left (x right )} – 156238908 sin^{6}{left (x right )} cos^{66}{left (x right )} + 5843376 sin^{6}{left (x right )} cos^{30}{left (x right )} + 1028790 sin^{4}{left (x right )} cos^{68}{left (x right )} – 176715 sin^{4}{left (x right )} cos^{32}{left (x right )} – 2556 sin^{2}{left (x right )} cos^{70}{left (x right )} + 1890 sin^{2}{left (x right )} cos^{34}{left (x right )} + cos^{72}{left (x right )} – 3 cos^{36}{left (x right )}$$
