На странице представлен фрагмент
Реши любую задачу с помощью нейросети.
Дано
$$sin{left (a right )} + cos{left (a right )} – frac{cos{left (a right )}}{sin{left (a right )}}$$
Подстановка условия
$$sin{left (a right )} + cos{left (a right )} – frac{cos{left (a right )}}{sin{left (a right )}}$$
cos((1/2)) + sin((1/2)) – cos((1/2))/sin((1/2))
$$sin{left ((1/2) right )} + cos{left ((1/2) right )} – frac{cos{left ((1/2) right )}}{sin{left ((1/2) right )}}$$
cos(1/2) + sin(1/2) – cos(1/2)/sin(1/2)
$$- frac{cos{left (frac{1}{2} right )}}{sin{left (frac{1}{2} right )}} + sin{left (frac{1}{2} right )} + cos{left (frac{1}{2} right )}$$
-cos(1/2)/sin(1/2) + cos(1/2) + sin(1/2)
$$- frac{cos{left (frac{1}{2} right )}}{sin{left (frac{1}{2} right )}} + sin{left (frac{1}{2} right )} + cos{left (frac{1}{2} right )}$$
Численный ответ
-cos(a)/sin(a) + cos(a) + sin(a)
Рациональный знаменатель
$$frac{1}{sin{left (a right )}} left(left(sin{left (a right )} + cos{left (a right )}right) sin{left (a right )} – cos{left (a right )}right)$$
Объединение рациональных выражений
$$frac{1}{sin{left (a right )}} left(left(sin{left (a right )} + cos{left (a right )}right) sin{left (a right )} – cos{left (a right )}right)$$
Общее упрощение
1 ___ / pi
– —— + / 2 *sin|a + –|
tan(a) 4 /
$$sqrt{2} sin{left (a + frac{pi}{4} right )} – frac{1}{tan{left (a right )}}$$
Соберем выражение
$$sin{left (a right )} + cos{left (a right )} – cot{left (a right )}$$
Тригонометрическая часть
1 ___ / pi
– —— + / 2 *sin|a + –|
tan(a) 4 /
$$sqrt{2} sin{left (a + frac{pi}{4} right )} – frac{1}{tan{left (a right )}}$$
Комбинаторика
2
sin (a) – cos(a) + cos(a)*sin(a)
——————————–
sin(a)
$$frac{1}{sin{left (a right )}} left(sin^{2}{left (a right )} + sin{left (a right )} cos{left (a right )} – cos{left (a right )}right)$$