Дано
$$frac{18}{cos{left (48 right )}} left(- cos^{24}{left (x right )} + sin^{2}{left (4 right )}right)$$
Подстановка условия
$$frac{18}{cos{left (48 right )}} left(- cos^{24}{left (x right )} + sin^{2}{left (4 right )}right)$$
(18*(sin(4)^2 – cos((1/3))^24))/cos(48)
$$frac{18}{cos{left (48 right )}} left(- cos^{24}{left ((1/3) right )} + sin^{2}{left (4 right )}right)$$
(18*(sin(4)^2 – cos(1/3)^24))/cos(48)
$$frac{18}{cos{left (48 right )}} left(- cos^{24}{left (frac{1}{3} right )} + sin^{2}{left (4 right )}right)$$
(-18*cos(1/3)^24 + 18*sin(4)^2)/cos(48)
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (frac{1}{3} right )} + 18 sin^{2}{left (4 right )}right)$$
Степени
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
Численный ответ
-16.1049620665646 + 28.1186583871466*cos(x)^24
Рациональный знаменатель
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
Объединение рациональных выражений
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
Общее упрощение
/ 2 24
18*sin (4) – cos (x)/
———————–
cos(48)
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
Соберем выражение
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
/1421113 735471*cos(8*x) 245157*cos(4*x) 156009*cos(2*x) 81719*cos(6*x) 43263*cos(10*x) 33649*cos(12*x) 5313*cos(14*x) 5313*cos(16*x) 253*cos(18*x) 69*cos(20*x) 3*cos(22*x) cos(8) cos(24*x)
18*|——- – ————— – ————— – ————— – ————– – ————— – ————— – ————– – ————– – ————- – ———— – ———– – —— – ———|*sec(48)
4194304 8388608 1048576 524288 524288 1048576 2097152 1048576 4194304 1048576 2097152 1048576 2 8388608 /
$$18 left(- frac{156009}{524288} cos{left (2 x right )} – frac{245157}{1048576} cos{left (4 x right )} – frac{81719}{524288} cos{left (6 x right )} – frac{735471}{8388608} cos{left (8 x right )} – frac{43263}{1048576} cos{left (10 x right )} – frac{33649}{2097152} cos{left (12 x right )} – frac{5313}{1048576} cos{left (14 x right )} – frac{5313}{4194304} cos{left (16 x right )} – frac{253}{1048576} cos{left (18 x right )} – frac{69}{2097152} cos{left (20 x right )} – frac{3}{1048576} cos{left (22 x right )} – frac{1}{8388608} cos{left (24 x right )} – frac{1}{2} cos{left (8 right )} + frac{1421113}{4194304}right) sec{left (48 right )}$$
Общий знаменатель
/ 2 24
– – 18*sin (4) + 18*cos (x)/
——————————
cos(48)
$$- frac{1}{cos{left (48 right )}} left(18 cos^{24}{left (x right )} – 18 sin^{2}{left (4 right )}right)$$
Тригонометрическая часть
/ 2 24
18*sin (4) – cos (x)/
———————–
cos(48)
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
Комбинаторика
/ 12 / 12
-18*cos (x) – sin(4)/*cos (x) + sin(4)/
——————————————-
cos(48)
$$- frac{18}{cos{left (48 right )}} left(cos^{12}{left (x right )} – sin{left (4 right )}right) left(cos^{12}{left (x right )} + sin{left (4 right )}right)$$
Раскрыть выражение
24 2
– 18*cos (x) + 18*sin (4)
————————–
cos(48)
$$frac{1}{cos{left (48 right )}} left(- 18 cos^{24}{left (x right )} + 18 sin^{2}{left (4 right )}right)$$
