(sin(8*a)+sin(2*a))*1/((cos(8*a)+cos(2*a)*cot(5)*a)^1) если a=2 (упростите выражение)

Выражение, которое надо упростить:
Например, 1/(a*x-1)-1/(a*x+1)

    Решение

    Вы ввели
    [LaTeX]
          sin(8*a) + sin(2*a)      
    -------------------------------
                                  1
    (cos(8*a) + cos(2*a)*cot(5)*a) 
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{\left(a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}\right)^{1}}$$
    Подстановка условия
    [LaTeX]
    (sin(8*a) + sin(2*a))/(cos(8*a) + (cos(2*a)*cot(5))*a)^1 при a = 2
    (sin(8*a) + sin(2*a))/(cos(8*a) + (cos(2*a)*cot(5))*a)^1
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{\left(a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}\right)^{1}}$$
    (sin(8*(2)) + sin(2*(2)))/(cos(8*(2)) + (cos(2*(2))*cot(5))*(2))^1
    $$\frac{\sin{\left (2 (2) \right )} + \sin{\left (8 (2) \right )}}{\left((2) \cos{\left (2 (2) \right )} \cot{\left (5 \right )} + \cos{\left (8 (2) \right )}\right)^{1}}$$
    (sin(8*2) + sin(2*2))/(cos(8*2) + (cos(2*2)*cot(5))*2)^1
    $$\frac{\sin{\left (2 \cdot 2 \right )} + \sin{\left (2 \cdot 8 \right )}}{\left(\cos{\left (2 \cdot 8 \right )} + 2 \cos{\left (2 \cdot 2 \right )} \cot{\left (5 \right )}\right)^{1}}$$
    (sin(4) + sin(16))/(2*cos(4)*cot(5) + cos(16))
    $$\frac{\sin{\left (4 \right )} + \sin{\left (16 \right )}}{\cos{\left (16 \right )} + 2 \cos{\left (4 \right )} \cot{\left (5 \right )}}$$
    Степени
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Численный ответ
    [LaTeX]
    (sin(2*a) + sin(8*a))/(-0.295812915532746*a*cos(2*a) + cos(8*a))
    Рациональный знаменатель
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Объединение рациональных выражений
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Общее упрощение
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Собрать выражение
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    cos(2*a)*cot(5)*a + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
              sin(2*a)                       sin(8*a)          
    ---------------------------- + ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)   a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}} + \frac{\sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Общий знаменатель
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Тригонометрическая часть
    [LaTeX]
        sin(8*a) + sin(2*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Комбинаторика
    [LaTeX]
        sin(2*a) + sin(8*a)     
    ----------------------------
    a*cos(2*a)*cot(5) + cos(8*a)
    $$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
    Раскрыть выражение
    [LaTeX]
                   5       3           7                                    7                   3       5          
           - 56*cos (a)*sin (a) - 8*sin (a)*cos(a) + 2*cos(a)*sin(a) + 8*cos (a)*sin(a) + 56*cos (a)*sin (a)       
    ---------------------------------------------------------------------------------------------------------------
       8         8            2       6            6       2            4       4        /   2         2   \       
    cos (a) + sin (a) - 28*cos (a)*sin (a) - 28*cos (a)*sin (a) + 70*cos (a)*sin (a) + a*\cos (a) - sin (a)/*cot(5)
    $$\frac{- 8 \sin^{7}{\left (a \right )} \cos{\left (a \right )} + 56 \sin^{5}{\left (a \right )} \cos^{3}{\left (a \right )} - 56 \sin^{3}{\left (a \right )} \cos^{5}{\left (a \right )} + 8 \sin{\left (a \right )} \cos^{7}{\left (a \right )} + 2 \sin{\left (a \right )} \cos{\left (a \right )}}{a \left(- \sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}\right) \cot{\left (5 \right )} + \sin^{8}{\left (a \right )} - 28 \sin^{6}{\left (a \right )} \cos^{2}{\left (a \right )} + 70 \sin^{4}{\left (a \right )} \cos^{4}{\left (a \right )} - 28 \sin^{2}{\left (a \right )} \cos^{6}{\left (a \right )} + \cos^{8}{\left (a \right )}}$$