sin(x)^4-cos(x)^2*sin(x)^2+cos(x)^4-sin(x)^6 если x=3 (упростите выражение)

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

    Решение

    Вы ввели
    [LaTeX]
       4         2       2         4         6   
    sin (x) - cos (x)*sin (x) + cos (x) - sin (x)
    $$\sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )} - \sin^{6}{\left (x \right )}$$
    Подстановка условия
    [LaTeX]
    sin(x)^4 - cos(x)^2*sin(x)^2 + cos(x)^4 - sin(x)^6 при x = 3
    sin(x)^4 - cos(x)^2*sin(x)^2 + cos(x)^4 - sin(x)^6
    $$\sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )} - \sin^{6}{\left (x \right )}$$
    sin((3))^4 - cos((3))^2*sin((3))^2 + cos((3))^4 - sin((3))^6
    $$\sin^{4}{\left ((3) \right )} - \sin^{2}{\left ((3) \right )} \cos^{2}{\left ((3) \right )} + \cos^{4}{\left ((3) \right )} - \sin^{6}{\left ((3) \right )}$$
    sin(3)^4 - cos(3)^2*sin(3)^2 + cos(3)^4 - sin(3)^6
    $$- \sin^{6}{\left (3 \right )} + - \sin^{2}{\left (3 \right )} \cos^{2}{\left (3 \right )} + \sin^{4}{\left (3 \right )} + \cos^{4}{\left (3 \right )}$$
    cos(3)^4 + sin(3)^4 - sin(3)^6 - cos(3)^2*sin(3)^2
    $$- \sin^{2}{\left (3 \right )} \cos^{2}{\left (3 \right )} - \sin^{6}{\left (3 \right )} + \sin^{4}{\left (3 \right )} + \cos^{4}{\left (3 \right )}$$
    Степени
    [LaTeX]
       4         4         6         2       2   
    cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
    $$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
    Численный ответ
    [LaTeX]
    cos(x)^4 + sin(x)^4 - sin(x)^6 - cos(x)^2*sin(x)^2
    Рациональный знаменатель
    [LaTeX]
       4         4         6         2       2   
    cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
    $$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
    Объединение рациональных выражений
    [LaTeX]
       4         6         2    /   2         2   \
    cos (x) - sin (x) + sin (x)*\sin (x) - cos (x)/
    $$\left(\sin^{2}{\left (x \right )} - \cos^{2}{\left (x \right )}\right) \sin^{2}{\left (x \right )} - \sin^{6}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
    Общее упрощение
    [LaTeX]
       6   
    cos (x)
    $$\cos^{6}{\left (x \right )}$$
    Собрать выражение
    [LaTeX]
    5    cos(6*x)   3*cos(4*x)   15*cos(2*x)
    -- + -------- + ---------- + -----------
    16      32          16            32    
    $$\frac{15}{32} \cos{\left (2 x \right )} + \frac{3}{16} \cos{\left (4 x \right )} + \frac{1}{32} \cos{\left (6 x \right )} + \frac{5}{16}$$
       4         4         6         2       2   
    cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
    $$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
    Общий знаменатель
    [LaTeX]
       4         4         6         2       2   
    cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
    $$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
    Тригонометрическая часть
    [LaTeX]
       6   
    cos (x)
    $$\cos^{6}{\left (x \right )}$$
    Комбинаторика
    [LaTeX]
       4         4         6         2       2   
    cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
    $$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
    Раскрыть выражение
    [LaTeX]
       4         4         6         2       2   
    cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
    $$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$