Дано
$$3 sin^{2}{left (x right )} – 3 sin{left (x right )} sin{left (2 x right )} + 9 cos^{2}{left (x right )} – 18 cos{left (x right )} cos{left (2 x right )} – 9 cos{left (x right )} + 18 cos{left (2 x right )}$$
Подстановка условия
$$3 sin^{2}{left (x right )} – 3 sin{left (x right )} sin{left (2 x right )} + 9 cos^{2}{left (x right )} – 18 cos{left (x right )} cos{left (2 x right )} – 9 cos{left (x right )} + 18 cos{left (2 x right )}$$
3*sin((-1/3))^2 – 3*sin((-1/3))*sin(2*(-1/3)) + 9*cos((-1/3))^2 – 18*cos((-1/3))*cos(2*(-1/3)) – 9*cos((-1/3)) + 18*cos(2*(-1/3))
$$3 sin^{2}{left ((-1/3) right )} – 3 sin{left ((-1/3) right )} sin{left (2 (-1/3) right )} + 9 cos^{2}{left ((-1/3) right )} – 18 cos{left ((-1/3) right )} cos{left (2 (-1/3) right )} – 9 cos{left ((-1/3) right )} + 18 cos{left (2 (-1/3) right )}$$
3*sin(-1/3)^2 – 3*sin(-1/3)*sin(2*(-1)/3) + 9*cos(-1/3)^2 – 18*cos(-1/3)*cos(2*(-1)/3) – 9*cos(-1/3) + 18*cos(2*(-1)/3)
$$- 9 cos{left (- frac{1}{3} right )} + – 18 cos{left (- frac{1}{3} right )} cos{left (frac{-2}{3} right )} + – 3 sin{left (- frac{1}{3} right )} sin{left (frac{-2}{3} right )} + 3 sin^{2}{left (- frac{1}{3} right )} + 9 cos^{2}{left (- frac{1}{3} right )} + 18 cos{left (frac{-2}{3} right )}$$
-9*cos(1/3) + 3*sin(1/3)^2 + 9*cos(1/3)^2 + 18*cos(2/3) – 18*cos(1/3)*cos(2/3) – 3*sin(1/3)*sin(2/3)
$$- 18 cos{left (frac{1}{3} right )} cos{left (frac{2}{3} right )} – 9 cos{left (frac{1}{3} right )} – 3 sin{left (frac{1}{3} right )} sin{left (frac{2}{3} right )} + 3 sin^{2}{left (frac{1}{3} right )} + 9 cos^{2}{left (frac{1}{3} right )} + 18 cos{left (frac{2}{3} right )}$$
Численный ответ
3.0*sin(x)^2 + 9.0*cos(x)^2 + 18.0*cos(2*x) – 9.0*cos(x) – 3.0*sin(x)*sin(2*x) – 18.0*cos(x)*cos(2*x)
Объединение рациональных выражений
$$3 left(left(sin{left (x right )} – sin{left (2 x right )}right) sin{left (x right )} + 3 cos^{2}{left (x right )} – 6 cos{left (x right )} cos{left (2 x right )} – 3 cos{left (x right )} + 6 cos{left (2 x right )}right)$$
Общее упрощение
39*cos(x) 15*cos(3*x)
6 + 21*cos(2*x) – ——— – ———–
2 2
$$- frac{39}{2} cos{left (x right )} + 21 cos{left (2 x right )} – frac{15}{2} cos{left (3 x right )} + 6$$
Соберем выражение
$$3 sin^{2}{left (x right )} – 3 sin{left (x right )} sin{left (2 x right )} + 9 cos^{2}{left (x right )} – 9 cos{left (x right )} – 18 cos{left (x right )} cos{left (2 x right )} + 18 cos{left (2 x right )}$$
39*cos(x) 15*cos(3*x)
6 + 21*cos(2*x) – ——— – ———–
2 2
$$- frac{39}{2} cos{left (x right )} + 21 cos{left (2 x right )} – frac{15}{2} cos{left (3 x right )} + 6$$
Тригонометрическая часть
2 39*cos(x) 15*cos(3*x)
27 – 42*sin (x) – ——— – ———–
2 2
$$- 42 sin^{2}{left (x right )} – frac{39}{2} cos{left (x right )} – frac{15}{2} cos{left (3 x right )} + 27$$
Комбинаторика
/ 2 2
-3* – sin (x) – 6*cos(2*x) – 3*cos (x) + 3*cos(x) + sin(x)*sin(2*x) + 6*cos(x)*cos(2*x)/
$$- 3 left(- sin^{2}{left (x right )} + sin{left (x right )} sin{left (2 x right )} – 3 cos^{2}{left (x right )} + 6 cos{left (x right )} cos{left (2 x right )} + 3 cos{left (x right )} – 6 cos{left (2 x right )}right)$$
