sqrt((8*sin(2*t)*cos(t))^2+(-4*cos(t)^3)^2+(64*cos(t)^2)^2) если t=-1 (упростите выражение)

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

    Решение

    Вы ввели
    [LaTeX]
        ______________________________________________________
       /                                    2               2 
      /                     2   /      3   \    /      2   \  
    \/   (8*sin(2*t)*cos(t))  + \-4*cos (t)/  + \64*cos (t)/  
    $$\sqrt{\left(8 \sin{\left (2 t \right )} \cos{\left (t \right )}\right)^{2} + \left(- 4 \cos^{3}{\left (t \right )}\right)^{2} + \left(64 \cos^{2}{\left (t \right )}\right)^{2}}$$
    Подстановка условия
    [LaTeX]
    sqrt(((8*sin(2*t))*cos(t))^2 + (-4*cos(t)^3)^2 + (64*cos(t)^2)^2) при t = -1
    sqrt(((8*sin(2*t))*cos(t))^2 + (-4*cos(t)^3)^2 + (64*cos(t)^2)^2)
    $$\sqrt{\left(8 \sin{\left (2 t \right )} \cos{\left (t \right )}\right)^{2} + \left(- 4 \cos^{3}{\left (t \right )}\right)^{2} + \left(64 \cos^{2}{\left (t \right )}\right)^{2}}$$
    sqrt(((8*sin(2*(-1)))*cos((-1)))^2 + (-4*cos((-1))^3)^2 + (64*cos((-1))^2)^2)
    $$\sqrt{\left(8 \sin{\left (2 (-1) \right )} \cos{\left ((-1) \right )}\right)^{2} + \left(- 4 \cos^{3}{\left ((-1) \right )}\right)^{2} + \left(64 \cos^{2}{\left ((-1) \right )}\right)^{2}}$$
    sqrt(((8*sin(2*(-1)))*cos(-1))^2 + (-4*cos(-1)^3)^2 + (64*cos(-1)^2)^2)
    $$\sqrt{\left(- 4 \cos^{3}{\left (-1 \right )}\right)^{2} + \left(8 \sin{\left (-1 \cdot 2 \right )} \cos{\left (-1 \right )}\right)^{2} + \left(64 \cos^{2}{\left (-1 \right )}\right)^{2}}$$
    sqrt(16*cos(1)^6 + 4096*cos(1)^4 + 64*cos(1)^2*sin(2)^2)
    $$\sqrt{16 \cos^{6}{\left (1 \right )} + 64 \sin^{2}{\left (2 \right )} \cos^{2}{\left (1 \right )} + 4096 \cos^{4}{\left (1 \right )}}$$
    Степени
    [LaTeX]
       __________________________________________________
      /       6              4            2       2      
    \/  16*cos (t) + 4096*cos (t) + 64*cos (t)*sin (2*t) 
    $$\sqrt{64 \sin^{2}{\left (2 t \right )} \cos^{2}{\left (t \right )} + 16 \cos^{6}{\left (t \right )} + 4096 \cos^{4}{\left (t \right )}}$$
    Численный ответ
    [LaTeX]
    (16.0*cos(t)^6 + 4096.0*cos(t)^4 + 64.0*cos(t)^2*sin(2*t)^2)^0.5
    Рациональный знаменатель
    [LaTeX]
       __________________________________________________
      /       6              4            2       2      
    \/  16*cos (t) + 4096*cos (t) + 64*cos (t)*sin (2*t) 
    $$\sqrt{64 \sin^{2}{\left (2 t \right )} \cos^{2}{\left (t \right )} + 16 \cos^{6}{\left (t \right )} + 4096 \cos^{4}{\left (t \right )}}$$
    Объединение рациональных выражений
    [LaTeX]
         _______________________________________________
        /    2    /   4           2               2   \ 
    4*\/  cos (t)*\cos (t) + 4*sin (2*t) + 256*cos (t)/ 
    $$4 \sqrt{\left(4 \sin^{2}{\left (2 t \right )} + \cos^{4}{\left (t \right )} + 256 \cos^{2}{\left (t \right )}\right) \cos^{2}{\left (t \right )}}$$
    Общее упрощение
    [LaTeX]
         ____________________________
        /    4    /            2   \ 
    4*\/  cos (t)*\272 - 15*cos (t)/ 
    $$4 \sqrt{\left(- 15 \cos^{2}{\left (t \right )} + 272\right) \cos^{4}{\left (t \right )}}$$
    Собрать выражение
    [LaTeX]
        _____________________________________________________
       /             2                                       
      /  /      3   \                       2           4    
    \/   \-4*cos (t)/  + (8*sin(2*t)*cos(t))  + 4096*cos (t) 
    $$\sqrt{\left(8 \sin{\left (2 t \right )} \cos{\left (t \right )}\right)^{2} + 4096 \cos^{4}{\left (t \right )} + \left(- 4 \cos^{3}{\left (t \right )}\right)^{2}}$$
        ___________________________________________________
       /                       15*cos(6*t)   4127*cos(2*t) 
      /  1557 + 499*cos(4*t) - ----------- + ------------- 
    \/                              2              2       
    $$\sqrt{\frac{4127}{2} \cos{\left (2 t \right )} + 499 \cos{\left (4 t \right )} - \frac{15}{2} \cos{\left (6 t \right )} + 1557}$$
    Общий знаменатель
    [LaTeX]
         _____________________________________________
        /    6             4           2       2      
    4*\/  cos (t) + 256*cos (t) + 4*cos (t)*sin (2*t) 
    $$4 \sqrt{4 \sin^{2}{\left (2 t \right )} \cos^{2}{\left (t \right )} + \cos^{6}{\left (t \right )} + 256 \cos^{4}{\left (t \right )}}$$
    Тригонометрическая часть
    [LaTeX]
       ______________________________
      /          6              4    
    \/  - 240*cos (t) + 4352*cos (t) 
    $$\sqrt{- 240 \cos^{6}{\left (t \right )} + 4352 \cos^{4}{\left (t \right )}}$$
    Комбинаторика
    [LaTeX]
         _______________________________________________
        /    2    /   4           2               2   \ 
    4*\/  cos (t)*\cos (t) + 4*sin (2*t) + 256*cos (t)/ 
    $$4 \sqrt{\left(4 \sin^{2}{\left (2 t \right )} + \cos^{4}{\left (t \right )} + 256 \cos^{2}{\left (t \right )}\right) \cos^{2}{\left (t \right )}}$$
    Раскрыть выражение
    [LaTeX]
       __________________________________________________
      /       6              4         2          2      
    \/  16*cos (t) + 4096*cos (t) + cos (t)*64*sin (2*t) 
    $$\sqrt{64 \sin^{2}{\left (2 t \right )} \cos^{2}{\left (t \right )} + 16 \cos^{6}{\left (t \right )} + 4096 \cos^{4}{\left (t \right )}}$$
       _________________________________________________
      /       6              4             4       2    
    \/  16*cos (t) + 4096*cos (t) + 256*cos (t)*sin (t) 
    $$\sqrt{256 \sin^{2}{\left (t \right )} \cos^{4}{\left (t \right )} + 16 \cos^{6}{\left (t \right )} + 4096 \cos^{4}{\left (t \right )}}$$