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Реши любую задачу с помощью нейросети.
Дано
$$- sin{left (x – 45 right )} cos{left (x + 45 right )} + sin{left (x + 45 right )} cos{left (x – 45 right )} – 1$$
Подстановка условия
$$- sin{left (x – 45 right )} cos{left (x + 45 right )} + sin{left (x + 45 right )} cos{left (x – 45 right )} – 1$$
sin((-3) + 45)*cos((-3) – 45) – cos((-3) + 45)*sin((-3) – 45) – 1
$$- sin{left ((-3) – 45 right )} cos{left ((-3) + 45 right )} + sin{left ((-3) + 45 right )} cos{left ((-3) – 45 right )} – 1$$
sin(-3 + 45)*cos(-3 – 45) – cos(-3 + 45)*sin(-3 – 45) – 1
$$-1 + – sin{left (-45 – 3 right )} cos{left (-3 + 45 right )} + sin{left (-3 + 45 right )} cos{left (-45 – 3 right )}$$
-1 + cos(42)*sin(48) + cos(48)*sin(42)
$$-1 + sin{left (48 right )} cos{left (42 right )} + sin{left (42 right )} cos{left (48 right )}$$
Численный ответ
-1.0 + cos(x – 45)*sin(x + 45) – cos(x + 45)*sin(x – 45)
Общее упрощение
-1 + sin(90)
$$-1 + sin{left (90 right )}$$
Соберем выражение
$$-1 + sin{left (90 right )}$$
Тригонометрическая часть
-1 + sin(90)
$$-1 + sin{left (90 right )}$$
Раскрыть выражение
-1 + (cos(45)*cos(x) + sin(45)*sin(x))*(cos(45)*sin(x) + cos(x)*sin(45)) – (cos(45)*cos(x) – sin(45)*sin(x))*(cos(45)*sin(x) – cos(x)*sin(45))
$$- left(- sin{left (45 right )} sin{left (x right )} + cos{left (45 right )} cos{left (x right )}right) left(sin{left (x right )} cos{left (45 right )} – sin{left (45 right )} cos{left (x right )}right) + left(sin{left (45 right )} sin{left (x right )} + cos{left (45 right )} cos{left (x right )}right) left(sin{left (x right )} cos{left (45 right )} + sin{left (45 right )} cos{left (x right )}right) – 1$$