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

Учитель очень удивится увидев твоё верное решение 😼

Решение

Вы ввели [src]
    ______________________________________________________
   /                                    2               2 
  /                     2   /      3   \    /      2   \  
\/   (8*sin(2*t)*cos(t))  + \-4*cos (t)/  + \64*cos (t)/  
(8sin(2t)cos(t))2+(4cos3(t))2+(64cos2(t))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}}
Подстановка условия [src]
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)
(8sin(2t)cos(t))2+(4cos3(t))2+(64cos2(t))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)
(8sin(2(1))cos((1)))2+(4cos3((1)))2+(64cos2((1)))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)
(4cos3(1))2+(8sin(12)cos(1))2+(64cos2(1))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)
16cos6(1)+64sin2(2)cos2(1)+4096cos4(1)\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 [src]
   __________________________________________________
  /       6              4            2       2      
\/  16*cos (t) + 4096*cos (t) + 64*cos (t)*sin (2*t) 
64sin2(2t)cos2(t)+16cos6(t)+4096cos4(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 [src]
(16.0*cos(t)^6 + 4096.0*cos(t)^4 + 64.0*cos(t)^2*sin(2*t)^2)^0.5
Рациональный знаменатель [src]
   __________________________________________________
  /       6              4            2       2      
\/  16*cos (t) + 4096*cos (t) + 64*cos (t)*sin (2*t) 
64sin2(2t)cos2(t)+16cos6(t)+4096cos4(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 [src]
     _______________________________________________
    /    2    /   4           2               2   \ 
4*\/  cos (t)*\cos (t) + 4*sin (2*t) + 256*cos (t)/ 
4(4sin2(2t)+cos4(t)+256cos2(t))cos2(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 [src]
     ____________________________
    /    4    /            2   \ 
4*\/  cos (t)*\272 - 15*cos (t)/ 
4(15cos2(t)+272)cos4(t)4 \sqrt{\left(- 15 \cos^{2}{\left (t \right )} + 272\right) \cos^{4}{\left (t \right )}}
Собрать выражение [src]
    _____________________________________________________
   /             2                                       
  /  /      3   \                       2           4    
\/   \-4*cos (t)/  + (8*sin(2*t)*cos(t))  + 4096*cos (t) 
(8sin(2t)cos(t))2+4096cos4(t)+(4cos3(t))2\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       
41272cos(2t)+499cos(4t)152cos(6t)+1557\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 [src]
     _____________________________________________
    /    6             4           2       2      
4*\/  cos (t) + 256*cos (t) + 4*cos (t)*sin (2*t) 
44sin2(2t)cos2(t)+cos6(t)+256cos4(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 [src]
   ______________________________
  /          6              4    
\/  - 240*cos (t) + 4352*cos (t) 
240cos6(t)+4352cos4(t)\sqrt{- 240 \cos^{6}{\left (t \right )} + 4352 \cos^{4}{\left (t \right )}}
Комбинаторика [src]
     _______________________________________________
    /    2    /   4           2               2   \ 
4*\/  cos (t)*\cos (t) + 4*sin (2*t) + 256*cos (t)/ 
4(4sin2(2t)+cos4(t)+256cos2(t))cos2(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 [src]
   __________________________________________________
  /       6              4         2          2      
\/  16*cos (t) + 4096*cos (t) + cos (t)*64*sin (2*t) 
64sin2(2t)cos2(t)+16cos6(t)+4096cos4(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) 
256sin2(t)cos4(t)+16cos6(t)+4096cos4(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 )}}