Дано
$$sin{left (90 right )} sin{left (x right )} + cos{left (90 right )} cos{left (x right )} – sin{left (x right )} cos{left (90 right )} – sin{left (90 right )} cos{left (x right )}$$
Подстановка условия
$$sin{left (90 right )} sin{left (x right )} + cos{left (90 right )} cos{left (x right )} – sin{left (x right )} cos{left (90 right )} – sin{left (90 right )} cos{left (x right )}$$
cos((-1))*cos(90) + sin((-1))*sin(90) – sin((-1))*cos(90) – cos((-1))*sin(90)
$$sin{left (90 right )} sin{left ((-1) right )} + cos{left (90 right )} cos{left ((-1) right )} – sin{left ((-1) right )} cos{left (90 right )} – sin{left (90 right )} cos{left ((-1) right )}$$
cos(-1)*cos(90) + sin(-1)*sin(90) – sin(-1)*cos(90) – cos(-1)*sin(90)
$$sin{left (-1 right )} sin{left (90 right )} + cos{left (-1 right )} cos{left (90 right )} – sin{left (-1 right )} cos{left (90 right )} – sin{left (90 right )} cos{left (-1 right )}$$
cos(1)*cos(90) + cos(90)*sin(1) – cos(1)*sin(90) – sin(1)*sin(90)
$$- sin{left (1 right )} sin{left (90 right )} – sin{left (90 right )} cos{left (1 right )} + sin{left (1 right )} cos{left (90 right )} + cos{left (1 right )} cos{left (90 right )}$$
Степени
$$- sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} sin{left (x right )} – sin{left (90 right )} cos{left (x right )} + cos{left (90 right )} cos{left (x right )}$$
Численный ответ
1.34207027972973*sin(x) – 1.34207027972973*cos(x)
Рациональный знаменатель
$$- sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} sin{left (x right )} – sin{left (90 right )} cos{left (x right )} + cos{left (90 right )} cos{left (x right )}$$
Объединение рациональных выражений
$$- sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} sin{left (x right )} – sin{left (90 right )} cos{left (x right )} + cos{left (90 right )} cos{left (x right )}$$
Общее упрощение
-sin(90 + x) + cos(-90 + x)
$$- sin{left (x + 90 right )} + cos{left (x – 90 right )}$$
Соберем выражение
$$- sin{left (x + 90 right )} + cos{left (x – 90 right )}$$
cos(x)*cos(90) + sin(x)*sin(90) – cos(x)*sin(90) – sin(x)*cos(90)
$$- sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} sin{left (x right )} – sin{left (90 right )} cos{left (x right )} + cos{left (90 right )} cos{left (x right )}$$
Общий знаменатель
cos(90)*cos(x) + sin(90)*sin(x) – cos(90)*sin(x) – cos(x)*sin(90)
$$- sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} sin{left (x right )} – sin{left (90 right )} cos{left (x right )} + cos{left (90 right )} cos{left (x right )}$$
Тригонометрическая часть
-sin(90 + x) + cos(-90 + x)
$$- sin{left (x + 90 right )} + cos{left (x – 90 right )}$$
Комбинаторика
(-sin(90) + cos(90))*(-sin(x) + cos(x))
$$left(- sin{left (90 right )} + cos{left (90 right )}right) left(- sin{left (x right )} + cos{left (x right )}right)$$
Раскрыть выражение
cos(90)*cos(x) + sin(90)*sin(x) – cos(90)*sin(x) – cos(x)*sin(90)
$$- sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} sin{left (x right )} – sin{left (90 right )} cos{left (x right )} + cos{left (90 right )} cos{left (x right )}$$