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