Дано
$$frac{- cos{left (2 a right )} + 1 + sin{left (2 a right )}}{cos{left (2 a right )} + 1 + sin{left (2 a right )}}$$
Подстановка условия
$$frac{- cos{left (2 a right )} + 1 + sin{left (2 a right )}}{cos{left (2 a right )} + 1 + sin{left (2 a right )}}$$
(1 – cos(2*(-2)) + sin(2*(-2)))/(1 + cos(2*(-2)) + sin(2*(-2)))
$$frac{- cos{left (2 (-2) right )} + 1 + sin{left (2 (-2) right )}}{cos{left (2 (-2) right )} + 1 + sin{left (2 (-2) right )}}$$
(1 – cos(2*(-2)) + sin(2*(-2)))/(1 + cos(2*(-2)) + sin(2*(-2)))
$$frac{sin{left (-2 cdot 2 right )} + – cos{left (-2 cdot 2 right )} + 1}{cos{left (-2 cdot 2 right )} + 1 + sin{left (-2 cdot 2 right )}}$$
(1 – cos(4) – sin(4))/(1 – sin(4) + cos(4))
$$frac{- cos{left (4 right )} – sin{left (4 right )} + 1}{cos{left (4 right )} – sin{left (4 right )} + 1}$$
Степени
$$frac{sin{left (2 a right )} – cos{left (2 a right )} + 1}{sin{left (2 a right )} + cos{left (2 a right )} + 1}$$
Численный ответ
(1.0 – cos(2*a) + sin(2*a))/(1.0 + cos(2*a) + sin(2*a))
Рациональный знаменатель
$$frac{sin{left (2 a right )} – cos{left (2 a right )} + 1}{sin{left (2 a right )} + cos{left (2 a right )} + 1}$$
Объединение рациональных выражений
$$frac{sin{left (2 a right )} – cos{left (2 a right )} + 1}{sin{left (2 a right )} + cos{left (2 a right )} + 1}$$
Общее упрощение
___ / pi
1 – / 2 *cos|2*a + –|
4 /
———————–
___ / pi
1 + / 2 *sin|2*a + –|
4 /
$$frac{- sqrt{2} cos{left (2 a + frac{pi}{4} right )} + 1}{sqrt{2} sin{left (2 a + frac{pi}{4} right )} + 1}$$
Соберем выражение
$$frac{sin{left (2 a right )} – cos{left (2 a right )} + 1}{sin{left (2 a right )} + cos{left (2 a right )} + 1}$$
1 sin(2*a) cos(2*a)
———————– + ———————– – ———————–
1 + cos(2*a) + sin(2*a) 1 + cos(2*a) + sin(2*a) 1 + cos(2*a) + sin(2*a)
$$frac{sin{left (2 a right )}}{sin{left (2 a right )} + cos{left (2 a right )} + 1} – frac{cos{left (2 a right )}}{sin{left (2 a right )} + cos{left (2 a right )} + 1} + frac{1}{sin{left (2 a right )} + cos{left (2 a right )} + 1}$$
Общий знаменатель
2 + 2*sin(2*a)
-1 + ———————–
1 + cos(2*a) + sin(2*a)
$$frac{2 sin{left (2 a right )} + 2}{sin{left (2 a right )} + cos{left (2 a right )} + 1} – 1$$
Тригонометрическая часть
___ / pi
1 – / 2 *cos|2*a + –|
4 /
———————–
___ / pi
1 + / 2 *sin|2*a + –|
4 /
$$frac{- sqrt{2} cos{left (2 a + frac{pi}{4} right )} + 1}{sqrt{2} sin{left (2 a + frac{pi}{4} right )} + 1}$$
Комбинаторика
-(-1 – sin(2*a) + cos(2*a))
—————————-
1 + cos(2*a) + sin(2*a)
$$- frac{- sin{left (2 a right )} + cos{left (2 a right )} – 1}{sin{left (2 a right )} + cos{left (2 a right )} + 1}$$
Раскрыть выражение
2 2
1 + sin (a) – cos (a) + 2*cos(a)*sin(a)
—————————————
2 2
1 + cos (a) – sin (a) + 2*cos(a)*sin(a)
$$frac{sin^{2}{left (a right )} + 2 sin{left (a right )} cos{left (a right )} – cos^{2}{left (a right )} + 1}{- sin^{2}{left (a right )} + 2 sin{left (a right )} cos{left (a right )} + cos^{2}{left (a right )} + 1}$$
