Дано
$$left(- frac{16 pi}{3} sin{left (frac{pi x^{2}}{6} right )} + frac{x}{3} pi left(- 16 cos{left (frac{pi x^{2}}{6} right )}right)right)^{2} + left(- frac{16 pi}{3} cos{left (frac{pi x^{2}}{6} right )} + frac{x}{3} pi 16 sin{left (frac{pi x^{2}}{6} right )}right)^{2}$$
Подстановка условия
$$left(- frac{16 pi}{3} sin{left (frac{pi x^{2}}{6} right )} + frac{x}{3} pi left(- 16 cos{left (frac{pi x^{2}}{6} right )}right)right)^{2} + left(- frac{16 pi}{3} cos{left (frac{pi x^{2}}{6} right )} + frac{x}{3} pi 16 sin{left (frac{pi x^{2}}{6} right )}right)^{2}$$
((((16*sin((pi*(-4)^2)/6))*pi)*(-4))/3 – (16*pi)*cos((pi*(-4)^2)/6)/3)^2 + ((((-16*cos((pi*(-4)^2)/6))*pi)*(-4))/3 – (16*pi)*sin((pi*(-4)^2)/6)/3)^2
$$left(- frac{16 pi}{3} sin{left (frac{pi (-4)^{2}}{6} right )} + frac{(-4)}{3} pi left(- 16 cos{left (frac{pi (-4)^{2}}{6} right )}right)right)^{2} + left(- frac{16 pi}{3} cos{left (frac{pi (-4)^{2}}{6} right )} + frac{(-4)}{3} pi 16 sin{left (frac{pi (-4)^{2}}{6} right )}right)^{2}$$
((((16*sin((pi*(-4)^2)/6))*pi)*(-4))/3 – (16*pi)*cos((pi*(-4)^2)/6)/3)^2 + ((((-16*cos((pi*(-4)^2)/6))*pi)*(-4))/3 – (16*pi)*sin((pi*(-4)^2)/6)/3)^2
$$left(frac{-4}{3} pi left(- 16 cos{left (frac{left(-4right)^{2} pi}{6} right )}right) – frac{16 pi}{3} sin{left (frac{left(-4right)^{2} pi}{6} right )}right)^{2} + left(frac{-4}{3} pi 16 sin{left (frac{left(-4right)^{2} pi}{6} right )} – frac{16 pi}{3} cos{left (frac{left(-4right)^{2} pi}{6} right )}right)^{2}$$
(-32*pi/3 – 8*pi*sqrt(3)/3)^2 + (8*pi/3 – 32*pi*sqrt(3)/3)^2
$$left(- frac{32 pi}{3} – frac{8 pi}{3} sqrt{3}right)^{2} + left(- frac{32 pi}{3} sqrt{3} + frac{8 pi}{3}right)^{2}$$
Степени
$$left(frac{16 pi}{3} x sin{left (frac{pi x^{2}}{6} right )} – frac{16 pi}{3} cos{left (frac{pi x^{2}}{6} right )}right)^{2} + left(- frac{16 pi}{3} x cos{left (frac{pi x^{2}}{6} right )} – frac{16 pi}{3} sin{left (frac{pi x^{2}}{6} right )}right)^{2}$$
Численный ответ
(-16.7551608191456*cos((pi*x^2)/6) + 16.7551608191456*x*sin((pi*x^2)/6))^2 + (-16.7551608191456*sin((pi*x^2)/6) – 16.7551608191456*x*cos((pi*x^2)/6))^2
Рациональный знаменатель
$$frac{1}{9} left(256 left(pi x sin{left (frac{pi x^{2}}{6} right )} – pi cos{left (frac{pi x^{2}}{6} right )}right)^{2} + 256 left(pi x cos{left (frac{pi x^{2}}{6} right )} + pi sin{left (frac{pi x^{2}}{6} right )}right)^{2}right)$$
Объединение рациональных выражений
$$frac{256 pi^{2}}{9} left(left(x sin{left (frac{pi x^{2}}{6} right )} – cos{left (frac{pi x^{2}}{6} right )}right)^{2} + left(- x cos{left (frac{pi x^{2}}{6} right )} – sin{left (frac{pi x^{2}}{6} right )}right)^{2}right)$$
Общее упрощение
2 / 2
256*pi *1 + x /
—————-
9
$$frac{256 pi^{2}}{9} left(x^{2} + 1right)$$
Общий знаменатель
/ 2 / 2 / 2 / 2
2 2|pi*x | 2 2|pi*x | 2 2 2|pi*x | 2 2 2|pi*x |
256*pi *cos |—–| 256*pi *sin |—–| 256*pi *x *cos |—–| 256*pi *x *sin |—–|
6 / 6 / 6 / 6 /
——————- + ——————- + ———————- + ———————-
9 9 9 9
$$frac{256 pi^{2}}{9} x^{2} sin^{2}{left (frac{pi x^{2}}{6} right )} + frac{256 pi^{2}}{9} x^{2} cos^{2}{left (frac{pi x^{2}}{6} right )} + frac{256 pi^{2}}{9} sin^{2}{left (frac{pi x^{2}}{6} right )} + frac{256 pi^{2}}{9} cos^{2}{left (frac{pi x^{2}}{6} right )}$$
Тригонометрическая часть
2 / 2
256*pi *1 + x /
—————-
9
$$frac{256 pi^{2}}{9} left(x^{2} + 1right)$$
Комбинаторика
/ / 2 / 2
2 / 2 | 2|pi*x | 2|pi*x ||
256*pi *1 + x /*|cos |—–| + sin |—–||
6 / 6 //
——————————————–
9
$$frac{256 pi^{2}}{9} left(x^{2} + 1right) left(sin^{2}{left (frac{pi x^{2}}{6} right )} + cos^{2}{left (frac{pi x^{2}}{6} right )}right)$$
Раскрыть выражение
2 2
/ / 2 / 2 / / 2 / 2
| |pi*x | |pi*x || | |pi*x | |pi*x ||
| 16*pi*cos|—–| 16*pi*x*sin|—–|| | 16*pi*sin|—–| 16*pi*x*cos|—–||
| 6 / 6 /| | 6 / 6 /|
|- —————- + ——————| + |- —————- – ——————|
3 3 / 3 3 /
$$left(frac{16 pi}{3} x sin{left (frac{pi x^{2}}{6} right )} – frac{16 pi}{3} cos{left (frac{pi x^{2}}{6} right )}right)^{2} + left(- frac{16 pi}{3} x cos{left (frac{pi x^{2}}{6} right )} – frac{16 pi}{3} sin{left (frac{pi x^{2}}{6} right )}right)^{2}$$
