Дано
$$- cos{left (- 3 p + frac{x}{2} right )} + 1 – frac{1}{4} cos^{2}{left (x right )} + sin^{2}{left (x right )}$$
Подстановка условия
$$- cos{left (- 3 p + frac{x}{2} right )} + 1 – frac{1}{4} cos^{2}{left (x right )} + sin^{2}{left (x right )}$$
1 – cos((-1/3)/2 – 3*p) – cos((-1/3))^2/4 + sin((-1/3))^2
$$- cos{left (frac{(-1/3)}{2} – 3 p right )} + 1 – frac{1}{4} cos^{2}{left ((-1/3) right )} + sin^{2}{left ((-1/3) right )}$$
1 – cos(-1/6 – 3*p) – cos(-1/3)^2/4 + sin(-1/3)^2
$$- cos{left (- 3 p – frac{1}{6} right )} + 1 – frac{1}{4} cos^{2}{left (- frac{1}{3} right )} + sin^{2}{left (- frac{1}{3} right )}$$
1 + sin(1/3)^2 – cos(1/6 + 3*p) – cos(1/3)^2/4
$$- cos{left (3 p + frac{1}{6} right )} – frac{1}{4} cos^{2}{left (frac{1}{3} right )} + sin^{2}{left (frac{1}{3} right )} + 1$$
Степени
$$sin^{2}{left (x right )} – frac{1}{4} cos^{2}{left (x right )} – cos{left (3 p – frac{x}{2} right )} + 1$$
Численный ответ
1.0 + sin(x)^2 – cos(x/2 – 3*p) – 0.25*cos(x)^2
Рациональный знаменатель
$$frac{1}{4} left(4 sin^{2}{left (x right )} – cos^{2}{left (x right )} – 4 cos{left (3 p – frac{x}{2} right )} + 4right)$$
Объединение рациональных выражений
$$frac{1}{4} left(4 sin^{2}{left (x right )} – cos^{2}{left (x right )} – 4 cos{left (frac{1}{2} left(- 6 p + xright) right )} + 4right)$$
Общее упрощение
2
/ x 5*cos (x)
2 – cos|3*p – -| – ———
2/ 4
$$- frac{5}{4} cos^{2}{left (x right )} – cos{left (3 p – frac{x}{2} right )} + 2$$
Соберем выражение
$$- frac{5}{8} cos{left (2 x right )} – cos{left (3 p – frac{x}{2} right )} + frac{11}{8}$$
2
2 /x cos (x)
1 + sin (x) – cos|- – 3*p| – ——-
2 / 4
$$sin^{2}{left (x right )} – frac{1}{4} cos^{2}{left (x right )} – cos{left (- 3 p + frac{x}{2} right )} + 1$$
Общий знаменатель
2
2 / x cos (x)
1 + sin (x) – cos|3*p – -| – ——-
2/ 4
$$sin^{2}{left (x right )} – frac{1}{4} cos^{2}{left (x right )} – cos{left (3 p – frac{x}{2} right )} + 1$$
Комбинаторика
/ 2 2 / x
-|-4 + cos (x) – 4*sin (x) + 4*cos|3*p – -||
2//
———————————————
4
$$- frac{1}{4} left(- 4 sin^{2}{left (x right )} + cos^{2}{left (x right )} + 4 cos{left (3 p – frac{x}{2} right )} – 4right)$$
Тригонометрическая часть
2
/ x 5*cos (x)
2 – cos|3*p – -| – ———
2/ 4
$$- frac{5}{4} cos^{2}{left (x right )} – cos{left (3 p – frac{x}{2} right )} + 2$$
Раскрыть выражение
2
2 cos (x) /x /x
1 + sin (x) – ——- – cos|-|*cos(3*p) – sin|-|*sin(3*p)
4 2/ 2/
$$- sin{left (3 p right )} sin{left (frac{x}{2} right )} + sin^{2}{left (x right )} – cos{left (3 p right )} cos{left (frac{x}{2} right )} – frac{1}{4} cos^{2}{left (x right )} + 1$$
