(-cos(10*x)^2)*cos(20*x)*1/(sin(20*x)^2)-20*1/(20*sin(20*x))*cos(10*x)*sin(10*x) если x=-3/2 (упростите выражение)

$$- 20 sin{left (10 x right )} frac{1}{20 sin{left (20 x right )}} cos{left (10 x right )} + frac{cos{left (20 x right )}}{sin^{2}{left (20 x right )}} left(-1 cos^{2}{left (10 x right )}right)$$

$$- 20 sin{left (10 x right )} frac{1}{20 sin{left (20 x right )}} cos{left (10 x right )} + frac{cos{left (20 x right )}}{sin^{2}{left (20 x right )}} left(-1 cos^{2}{left (10 x right )}right)$$

((-cos(10*(-3/2))^2)*cos(20*(-3/2)))/sin(20*(-3/2))^2 – (20/(20*sin(20*(-3/2))))*cos(10*(-3/2))*sin(10*(-3/2))

$$- 20 sin{left (10 (-3/2) right )} frac{1}{20 sin{left (20 (-3/2) right )}} cos{left (10 (-3/2) right )} + frac{cos{left (20 (-3/2) right )}}{sin^{2}{left (20 (-3/2) right )}} left(-1 cos^{2}{left (10 (-3/2) right )}right)$$

((-cos(10*(-3)/2)^2)*cos(20*(-3)/2))/sin(20*(-3)/2)^2 – (20/(20*sin(20*(-3)/2)))*cos(10*(-3)/2)*sin(10*(-3)/2)

$$- 20 sin{left (frac{-30}{2} right )} frac{1}{20 sin{left (frac{-60}{2} right )}} cos{left (frac{-30}{2} right )} + frac{cos{left (frac{-60}{2} right )}}{sin^{2}{left (frac{-60}{2} right )}} left(-1 cos^{2}{left (frac{-30}{2} right )}right)$$

-cos(15)^2*cos(30)/sin(30)^2 – cos(15)*sin(15)/sin(30)

$$- frac{sin{left (15 right )} cos{left (15 right )}}{sin{left (30 right )}} – frac{cos^{2}{left (15 right )} cos{left (30 right )}}{sin^{2}{left (30 right )}}$$

$$- frac{sin{left (10 x right )} cos{left (10 x right )}}{sin{left (20 x right )}} – frac{cos^{2}{left (10 x right )} cos{left (20 x right )}}{sin^{2}{left (20 x right )}}$$

-1.0*cos(10*x)^2*cos(20*x)/sin(20*x)^2 – 1.0*cos(10*x)*sin(10*x)/sin(20*x)

$$frac{1}{20 sin^{3}{left (20 x right )}} left(- 20 sin{left (10 x right )} sin^{2}{left (20 x right )} cos{left (10 x right )} – 20 sin{left (20 x right )} cos^{2}{left (10 x right )} cos{left (20 x right )}right)$$

$$frac{cos{left (10 x right )}}{sin^{2}{left (20 x right )}} left(- sin{left (10 x right )} sin{left (20 x right )} – cos{left (10 x right )} cos{left (20 x right )}right)$$

1
—————-
-2 + 2*cos(20*x)

$$frac{1}{2 cos{left (20 x right )} – 2}$$

$$left(- frac{1}{2} cos{left (20 x right )} – frac{1}{2}right) cot{left (20 x right )} csc{left (20 x right )} – frac{1}{2}$$

/ 2
-cos (10*x)*cos(20*x) + cos(10*x)*sin(10*x)*sin(20*x)/
——————————————————–
2
sin (20*x)

$$- frac{1}{sin^{2}{left (20 x right )}} left(sin{left (10 x right )} sin{left (20 x right )} cos{left (10 x right )} + cos^{2}{left (10 x right )} cos{left (20 x right )}right)$$

-1
—————–
2*(1 – cos(20*x))

$$- frac{1}{- 2 cos{left (20 x right )} + 2}$$

-(cos(10*x)*cos(20*x) + sin(10*x)*sin(20*x))*cos(10*x)
——————————————————-
2
sin (20*x)

$$- frac{cos{left (10 x right )}}{sin^{2}{left (20 x right )}} left(sin{left (10 x right )} sin{left (20 x right )} + cos{left (10 x right )} cos{left (20 x right )}right)$$

2
-cos (10*x)*cos(20*x) cos(10*x)*sin(10*x)
——————— – ——————-
2 sin(20*x)
sin (20*x)

$$frac{cos{left (20 x right )}}{sin^{2}{left (20 x right )}} left(-1 cos^{2}{left (10 x right )}right) – frac{sin{left (10 x right )} cos{left (10 x right )}}{sin{left (20 x right )}}$$

2
/ 10 10 4 6 8 2 2 8 6 4 / 20 20 10 10 6 14 14 6 2 18 18 2 4 16 16 4 8 12 12 8 / 3 7 7 3 9 9 5 5 / 10 10 4 6 8 2 2 8 6 4
cos (x) – sin (x) – 210*cos (x)*sin (x) – 45*cos (x)*sin (x) + 45*cos (x)*sin (x) + 210*cos (x)*sin (x)/ *cos (x) + sin (x) – 184756*cos (x)*sin (x) – 38760*cos (x)*sin (x) – 38760*cos (x)*sin (x) – 190*cos (x)*sin (x) – 190*cos (x)*sin (x) + 4845*cos (x)*sin (x) + 4845*cos (x)*sin (x) + 125970*cos (x)*sin (x) + 125970*cos (x)*sin (x)/ – 120*cos (x)*sin (x) – 120*cos (x)*sin (x) + 10*cos (x)*sin(x) + 10*sin (x)*cos(x) + 252*cos (x)*sin (x)/*cos (x) – sin (x) – 210*cos (x)*sin (x) – 45*cos (x)*sin (x) + 45*cos (x)*sin (x) + 210*cos (x)*sin (x)/
– —————————————————————————————————————————————————————————————————————————————————————————————————————————————————————– – ————————————————————————————————————————————————————————————————————————————————-
2 9 11 13 7 5 15 17 3 19 19 3 17 15 5 7 13 11 9
/ 9 11 13 7 5 15 17 3 19 19 3 17 15 5 7 13 11 9 – 167960*cos (x)*sin (x) – 77520*cos (x)*sin (x) – 15504*cos (x)*sin (x) – 1140*cos (x)*sin (x) – 20*sin (x)*cos(x) + 20*cos (x)*sin(x) + 1140*cos (x)*sin (x) + 15504*cos (x)*sin (x) + 77520*cos (x)*sin (x) + 167960*cos (x)*sin (x)
– 167960*cos (x)*sin (x) – 77520*cos (x)*sin (x) – 15504*cos (x)*sin (x) – 1140*cos (x)*sin (x) – 20*sin (x)*cos(x) + 20*cos (x)*sin(x) + 1140*cos (x)*sin (x) + 15504*cos (x)*sin (x) + 77520*cos (x)*sin (x) + 167960*cos (x)*sin (x)/

$$- frac{left(10 sin^{9}{left (x right )} cos{left (x right )} – 120 sin^{7}{left (x right )} cos^{3}{left (x right )} + 252 sin^{5}{left (x right )} cos^{5}{left (x right )} – 120 sin^{3}{left (x right )} cos^{7}{left (x right )} + 10 sin{left (x right )} cos^{9}{left (x right )}right) left(- sin^{10}{left (x right )} + 45 sin^{8}{left (x right )} cos^{2}{left (x right )} – 210 sin^{6}{left (x right )} cos^{4}{left (x right )} + 210 sin^{4}{left (x right )} cos^{6}{left (x right )} – 45 sin^{2}{left (x right )} cos^{8}{left (x right )} + cos^{10}{left (x right )}right)}{- 20 sin^{19}{left (x right )} cos{left (x right )} + 1140 sin^{17}{left (x right )} cos^{3}{left (x right )} – 15504 sin^{15}{left (x right )} cos^{5}{left (x right )} + 77520 sin^{13}{left (x right )} cos^{7}{left (x right )} – 167960 sin^{11}{left (x right )} cos^{9}{left (x right )} + 167960 sin^{9}{left (x right )} cos^{11}{left (x right )} – 77520 sin^{7}{left (x right )} cos^{13}{left (x right )} + 15504 sin^{5}{left (x right )} cos^{15}{left (x right )} – 1140 sin^{3}{left (x right )} cos^{17}{left (x right )} + 20 sin{left (x right )} cos^{19}{left (x right )}} – frac{left(- sin^{10}{left (x right )} + 45 sin^{8}{left (x right )} cos^{2}{left (x right )} – 210 sin^{6}{left (x right )} cos^{4}{left (x right )} + 210 sin^{4}{left (x right )} cos^{6}{left (x right )} – 45 sin^{2}{left (x right )} cos^{8}{left (x right )} + cos^{10}{left (x right )}right)^{2} left(sin^{20}{left (x right )} – 190 sin^{18}{left (x right )} cos^{2}{left (x right )} + 4845 sin^{16}{left (x right )} cos^{4}{left (x right )} – 38760 sin^{14}{left (x right )} cos^{6}{left (x right )} + 125970 sin^{12}{left (x right )} cos^{8}{left (x right )} – 184756 sin^{10}{left (x right )} cos^{10}{left (x right )} + 125970 sin^{8}{left (x right )} cos^{12}{left (x right )} – 38760 sin^{6}{left (x right )} cos^{14}{left (x right )} + 4845 sin^{4}{left (x right )} cos^{16}{left (x right )} – 190 sin^{2}{left (x right )} cos^{18}{left (x right )} + cos^{20}{left (x right )}right)}{left(- 20 sin^{19}{left (x right )} cos{left (x right )} + 1140 sin^{17}{left (x right )} cos^{3}{left (x right )} – 15504 sin^{15}{left (x right )} cos^{5}{left (x right )} + 77520 sin^{13}{left (x right )} cos^{7}{left (x right )} – 167960 sin^{11}{left (x right )} cos^{9}{left (x right )} + 167960 sin^{9}{left (x right )} cos^{11}{left (x right )} – 77520 sin^{7}{left (x right )} cos^{13}{left (x right )} + 15504 sin^{5}{left (x right )} cos^{15}{left (x right )} – 1140 sin^{3}{left (x right )} cos^{17}{left (x right )} + 20 sin{left (x right )} cos^{19}{left (x right )}right)^{2}}$$