sin(a)^6+cos(a)^6+3*sin(a)^2*cos(a)^2 если a=3/2 (упростите выражение)

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

    Решение

    Вы ввели
    [LaTeX]
       6         6           2       2   
    sin (a) + cos (a) + 3*sin (a)*cos (a)
    $$\sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )}$$
    Подстановка условия
    [LaTeX]
    sin(a)^6 + cos(a)^6 + (3*sin(a)^2)*cos(a)^2 при a = 3/2
    sin(a)^6 + cos(a)^6 + (3*sin(a)^2)*cos(a)^2
    $$\sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )}$$
    sin((3/2))^6 + cos((3/2))^6 + (3*sin((3/2))^2)*cos((3/2))^2
    $$\sin^{6}{\left ((3/2) \right )} + \cos^{6}{\left ((3/2) \right )} + 3 \sin^{2}{\left ((3/2) \right )} \cos^{2}{\left ((3/2) \right )}$$
    sin(3/2)^6 + cos(3/2)^6 + (3*sin(3/2)^2)*cos(3/2)^2
    $$3 \sin^{2}{\left (\frac{3}{2} \right )} \cos^{2}{\left (\frac{3}{2} \right )} + \cos^{6}{\left (\frac{3}{2} \right )} + \sin^{6}{\left (\frac{3}{2} \right )}$$
    cos(3/2)^6 + sin(3/2)^6 + 3*cos(3/2)^2*sin(3/2)^2
    $$\cos^{6}{\left (\frac{3}{2} \right )} + 3 \sin^{2}{\left (\frac{3}{2} \right )} \cos^{2}{\left (\frac{3}{2} \right )} + \sin^{6}{\left (\frac{3}{2} \right )}$$
    Степени
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*cos (a)*sin (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    Численный ответ
    [LaTeX]
    cos(a)^6 + sin(a)^6 + 3.0*cos(a)^2*sin(a)^2
    Рациональный знаменатель
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*cos (a)*sin (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    Объединение рациональных выражений
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*cos (a)*sin (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    Общее упрощение
    [LaTeX]
    3      6         6      3*cos(4*a)
    - + cos (a) + sin (a) - ----------
    8                           8     
    $$\sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )} - \frac{3}{8} \cos{\left (4 a \right )} + \frac{3}{8}$$
    Собрать выражение
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*sin (a)*cos (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    1
    $$1$$
    Общий знаменатель
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*cos (a)*sin (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    Тригонометрическая часть
    [LaTeX]
       6         6      3*(1 - cos(4*a))
    cos (a) + sin (a) + ----------------
                               8        
    $$\frac{1}{8} \left(- 3 \cos{\left (4 a \right )} + 3\right) + \sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    Комбинаторика
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*cos (a)*sin (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
    Раскрыть выражение
    [LaTeX]
       6         6           2       2   
    cos (a) + sin (a) + 3*cos (a)*sin (a)
    $$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$