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Общий знаменатель -1/cos(x)+4*cos(x)-2*sin( ... os(x)^3+6*sin(x)^2/cos(x)

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Примеры

Решение

Вы ввели [src]
                           2           4           2   
    1                 2*sin (x)   4*sin (x)   6*sin (x)
- ------ + 4*cos(x) - --------- + --------- + ---------
  cos(x)                  3           3         cos(x) 
                       cos (x)     cos (x)
$$4 \cos{\left (x \right )} - \frac{1}{\cos{\left (x \right )}} - \frac{2 \sin^{2}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + \frac{4 \sin^{4}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + \frac{6 \sin^{2}{\left (x \right )}}{\cos{\left (x \right )}}$$
Степени [src]
                           2           4           2   
    1                 2*sin (x)   4*sin (x)   6*sin (x)
- ------ + 4*cos(x) - --------- + --------- + ---------
  cos(x)                  3           3         cos(x) 
                       cos (x)     cos (x)
$$\frac{4 \sin^{4}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + \frac{6 \sin^{2}{\left (x \right )}}{\cos{\left (x \right )}} - \frac{2 \sin^{2}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + 4 \cos{\left (x \right )} - \frac{1}{\cos{\left (x \right )}}$$
Численный ответ [src]
-1/cos(x) + 4.0*cos(x) + 4.0*sin(x)^4/cos(x)^3 + 6.0*sin(x)^2/cos(x) - 2.0*sin(x)^2/cos(x)^3
Рациональный знаменатель [src]
/   3    /   3    /          2   \        2          \        4       4   \               7       2   
\cos (x)*\cos (x)*\-1 + 4*cos (x)/ - 2*sin (x)*cos(x)/ + 4*cos (x)*sin (x)/*cos(x) + 6*cos (x)*sin (x)
------------------------------------------------------------------------------------------------------
                                                  8                                                   
                                               cos (x)
$$\frac{1}{\cos^{8}{\left (x \right )}} \left(\left(\left(\left(4 \cos^{2}{\left (x \right )} - 1\right) \cos^{3}{\left (x \right )} - 2 \sin^{2}{\left (x \right )} \cos{\left (x \right )}\right) \cos^{3}{\left (x \right )} + 4 \sin^{4}{\left (x \right )} \cos^{4}{\left (x \right )}\right) \cos{\left (x \right )} + 6 \sin^{2}{\left (x \right )} \cos^{7}{\left (x \right )}\right)$$
Объединение рациональных выражений [src]
       2           4         2    /          2   \        2       2   
- 2*sin (x) + 4*sin (x) + cos (x)*\-1 + 4*cos (x)/ + 6*cos (x)*sin (x)
----------------------------------------------------------------------
                                  3                                   
                               cos (x)
$$\frac{1}{\cos^{3}{\left (x \right )}} \left(\left(4 \cos^{2}{\left (x \right )} - 1\right) \cos^{2}{\left (x \right )} + 4 \sin^{4}{\left (x \right )} + 6 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} - 2 \sin^{2}{\left (x \right )}\right)$$
Общее упрощение [src]
         4   
    2*sin (x)
3 + ---------
        2    
     cos (x) 
-------------
    cos(x)
$$\frac{1}{\cos{\left (x \right )}} \left(\frac{2 \sin^{4}{\left (x \right )}}{\cos^{2}{\left (x \right )}} + 3\right)$$
Собрать выражение [src]
                           4           2           2   
    1                 4*sin (x)   6*sin (x)   2*sin (x)
- ------ + 4*cos(x) + --------- + --------- - ---------
  cos(x)                  3         cos(x)        3    
                       cos (x)                 cos (x)
$$- \frac{2 \sin^{2}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + \frac{6 \sin^{2}{\left (x \right )}}{\cos{\left (x \right )}} + \frac{4 \sin^{4}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + 4 \cos{\left (x \right )} - \frac{1}{\cos{\left (x \right )}}$$
                          2                  3                            
-sec(x) + 4*cos(x) - 2*tan (x)*sec(x) + 4*tan (x)*sin(x) + 6*sin(x)*tan(x)
$$4 \sin{\left (x \right )} \tan^{3}{\left (x \right )} + 6 \sin{\left (x \right )} \tan{\left (x \right )} + 4 \cos{\left (x \right )} - 2 \tan^{2}{\left (x \right )} \sec{\left (x \right )} - \sec{\left (x \right )}$$
Общий знаменатель [src]
                2           2           4           2       2   
           - cos (x) - 2*sin (x) + 4*sin (x) + 6*cos (x)*sin (x)
4*cos(x) + -----------------------------------------------------
                                     3                          
                                  cos (x)
$$\frac{1}{\cos^{3}{\left (x \right )}} \left(4 \sin^{4}{\left (x \right )} + 6 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} - 2 \sin^{2}{\left (x \right )} - \cos^{2}{\left (x \right )}\right) + 4 \cos{\left (x \right )}$$
Тригонометрическая часть [src]
         4   
    2*sin (x)
3 + ---------
        2    
     cos (x) 
-------------
    cos(x)
$$\frac{1}{\cos{\left (x \right )}} \left(\frac{2 \sin^{4}{\left (x \right )}}{\cos^{2}{\left (x \right )}} + 3\right)$$
Комбинаторика [src]
     2           2           4           4           2       2   
- cos (x) - 2*sin (x) + 4*cos (x) + 4*sin (x) + 6*cos (x)*sin (x)
-----------------------------------------------------------------
                                3                                
                             cos (x)
$$\frac{1}{\cos^{3}{\left (x \right )}} \left(4 \sin^{4}{\left (x \right )} + 6 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} - 2 \sin^{2}{\left (x \right )} + 4 \cos^{4}{\left (x \right )} - \cos^{2}{\left (x \right )}\right)$$
Раскрыть выражение [src]
                           2           4           2   
    1                 2*sin (x)   4*sin (x)   6*sin (x)
- ------ + 4*cos(x) - --------- + --------- + ---------
  cos(x)                  3           3         cos(x) 
                       cos (x)     cos (x)
$$\frac{4 \sin^{4}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + \frac{6 \sin^{2}{\left (x \right )}}{\cos{\left (x \right )}} - \frac{2 \sin^{2}{\left (x \right )}}{\cos^{3}{\left (x \right )}} + 4 \cos{\left (x \right )} - \frac{1}{\cos{\left (x \right )}}$$