Дано
$$frac{sin{left (a + 45 right )} – cos{left (a + 45 right )}}{sin{left (a + 45 right )} + cos{left (a + 45 right )}}$$
Подстановка условия
$$frac{sin{left (a + 45 right )} – cos{left (a + 45 right )}}{sin{left (a + 45 right )} + cos{left (a + 45 right )}}$$
(sin(45 + (-4)) – cos(45 + (-4)))/(sin(45 + (-4)) + cos(45 + (-4)))
$$frac{sin{left ((-4) + 45 right )} – cos{left ((-4) + 45 right )}}{sin{left ((-4) + 45 right )} + cos{left ((-4) + 45 right )}}$$
(sin(45 – 4) – cos(45 – 4))/(sin(45 – 4) + cos(45 – 4))
$$frac{sin{left (-4 + 45 right )} – cos{left (-4 + 45 right )}}{cos{left (-4 + 45 right )} + sin{left (-4 + 45 right )}}$$
(-cos(41) + sin(41))/(cos(41) + sin(41))
$$frac{sin{left (41 right )} – cos{left (41 right )}}{cos{left (41 right )} + sin{left (41 right )}}$$
Численный ответ
(-cos(45 + a) + sin(45 + a))/(cos(45 + a) + sin(45 + a))
Общее упрощение
-1
—————-
/ pi
tan|45 + a + –|
4 /
$$- frac{1}{tan{left (a + frac{pi}{4} + 45 right )}}$$
Общий знаменатель
2*sin(45 + a)
-1 + ————————-
cos(45 + a) + sin(45 + a)
$$-1 + frac{2 sin{left (a + 45 right )}}{sin{left (a + 45 right )} + cos{left (a + 45 right )}}$$
Тригонометрическая часть
-1
—————-
/ pi
tan|45 + a + –|
4 /
$$- frac{1}{tan{left (a + frac{pi}{4} + 45 right )}}$$
Комбинаторика
-(-sin(45 + a) + cos(45 + a))
——————————
cos(45 + a) + sin(45 + a)
$$- frac{- sin{left (a + 45 right )} + cos{left (a + 45 right )}}{sin{left (a + 45 right )} + cos{left (a + 45 right )}}$$
Раскрыть выражение
cos(45)*sin(a) + cos(a)*sin(45) + sin(45)*sin(a) – cos(45)*cos(a)
—————————————————————–
cos(45)*cos(a) + cos(45)*sin(a) + cos(a)*sin(45) – sin(45)*sin(a)
$$frac{sin{left (a right )} cos{left (45 right )} + sin{left (45 right )} sin{left (a right )} – cos{left (45 right )} cos{left (a right )} + sin{left (45 right )} cos{left (a right )}}{- sin{left (45 right )} sin{left (a right )} + sin{left (a right )} cos{left (45 right )} + cos{left (45 right )} cos{left (a right )} + sin{left (45 right )} cos{left (a right )}}$$