Descomposición de una fracción (cos²x)/(sinx-cosx)-((sinx-cosx)/(1-ctg²x))+sinx/tgx ((coseno de al cuadrado x) dividir por (seno de x menos coseno de x) menos ((seno de x menos coseno de x) dividir por (1 menos ctg al cuadrado x)) más seno de x dividir por tgx)

Ha introducido [src]

       2                                  
    cos (x)       sin(x) - cos(x)   sin(x)
--------------- - --------------- + ------
sin(x) - cos(x)            2        tan(x)
                    1 - cot (x)

$$\left(\frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}\right) + \frac{\sin{\left(x \right)}}{\tan{\left(x \right)}}$$

cos(x)^2/(sin(x) - cos(x)) - (sin(x) - cos(x))/(1 - cot(x)^2) + sin(x)/tan(x)

Simplificación general [src]

                          2                 
-cos(x) + sin(x)       cos (x)        sin(x)
---------------- + ---------------- + ------
          2        -cos(x) + sin(x)   tan(x)
  -1 + cot (x)

$$\frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\cot^{2}{\left(x \right)} - 1} + \frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}}$$

(-cos(x) + sin(x))/(-1 + cot(x)^2) + cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x)

Denominador racional [src]

/   2    /       2   \                                        \          /       2   \                          
\cos (x)*\1 - cot (x)/ + (-cos(x) + sin(x))*(-sin(x) + cos(x))/*tan(x) + \1 - cot (x)/*(-cos(x) + sin(x))*sin(x)
----------------------------------------------------------------------------------------------------------------
                                    /       2   \                                                               
                                    \1 - cot (x)/*(-cos(x) + sin(x))*tan(x)

$$\frac{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} + \left(\left(1 - \cot^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} + \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \tan{\left(x \right)}}{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \tan{\left(x \right)}}$$

((cos(x)^2*(1 - cot(x)^2) + (-cos(x) + sin(x))*(-sin(x) + cos(x)))*tan(x) + (1 - cot(x)^2)*(-cos(x) + sin(x))*sin(x))/((1 - cot(x)^2)*(-cos(x) + sin(x))*tan(x))

Denominador común [src]

                        2         2                2       2                         2       2                2                                          
                   - sin (x) + cos (x)*tan(x) + cot (x)*sin (x) + cos(x)*sin(x) + cot (x)*sin (x)*tan(x) - cot (x)*cos(x)*sin(x) - 2*cos(x)*sin(x)*tan(x)
-cos(x) - sin(x) - --------------------------------------------------------------------------------------------------------------------------------------
                                                                                  2                       2                                              
                                               sin(x)*tan(x) - cos(x)*tan(x) + cot (x)*cos(x)*tan(x) - cot (x)*sin(x)*tan(x)

$$- \sin{\left(x \right)} - \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} + \sin^{2}{\left(x \right)} \cot^{2}{\left(x \right)} - \sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} \cot^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{- \sin{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} + \sin{\left(x \right)} \tan{\left(x \right)} + \cos{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} - \cos{\left(x \right)} \tan{\left(x \right)}}$$

-cos(x) - sin(x) - (-sin(x)^2 + cos(x)^2*tan(x) + cot(x)^2*sin(x)^2 + cos(x)*sin(x) + cot(x)^2*sin(x)^2*tan(x) - cot(x)^2*cos(x)*sin(x) - 2*cos(x)*sin(x)*tan(x))/(sin(x)*tan(x) - cos(x)*tan(x) + cot(x)^2*cos(x)*tan(x) - cot(x)^2*sin(x)*tan(x))

Potencias [src]

       2                                    
    cos (x)        sin(x)   -cos(x) + sin(x)
---------------- + ------ - ----------------
-cos(x) + sin(x)   tan(x)            2      
                              1 - cot (x)

$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$

                          2                 
-sin(x) + cos(x)       cos (x)        sin(x)
---------------- + ---------------- + ------
         2         -cos(x) + sin(x)   tan(x)
  1 - cot (x)

$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} + \frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$

                        2                                                                                  
          / I*x    -I*x\                 I*x    -I*x     /   -I*x    I*x\                                  
          |e      e    |                e      e       I*\- e     + e   /                                  
          |---- + -----|              - ---- - ----- - ------------------   /   -I*x    I*x\ / I*x    -I*x\
          \ 2       2  /                 2       2             2            \- e     + e   /*\e    + e    /
----------------------------------- - ----------------------------------- - -------------------------------
   I*x    -I*x     /   -I*x    I*x\                      2                           /   I*x    -I*x\      
  e      e       I*\- e     + e   /               1 - cot (x)                      2*\- e    + e    /      
- ---- - ----- - ------------------                                                                        
   2       2             2

$$\frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} - \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}} - \frac{\left(e^{i x} - e^{- i x}\right) \left(e^{i x} + e^{- i x}\right)}{2 \left(- e^{i x} + e^{- i x}\right)} - \frac{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} - \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}}{1 - \cot^{2}{\left(x \right)}}$$

(exp(i*x)/2 + exp(-i*x)/2)^2/(-exp(i*x)/2 - exp(-i*x)/2 - i*(-exp(-i*x) + exp(i*x))/2) - (-exp(i*x)/2 - exp(-i*x)/2 - i*(-exp(-i*x) + exp(i*x))/2)/(1 - cot(x)^2) - (-exp(-i*x) + exp(i*x))*(exp(i*x) + exp(-i*x))/(2*(-exp(i*x) + exp(-i*x)))

Combinatoria [src]

 /     2         2       2         2                                2       2                2                                          \ 
-\- sin (x) + cot (x)*sin (x) + sin (x)*tan(x) + cos(x)*sin(x) + cos (x)*cot (x)*tan(x) - cot (x)*cos(x)*sin(x) - 2*cos(x)*sin(x)*tan(x)/ 
------------------------------------------------------------------------------------------------------------------------------------------
                                           (1 + cot(x))*(-1 + cot(x))*(-sin(x) + cos(x))*tan(x)

$$- \frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)} + \sin^{2}{\left(x \right)} \cot^{2}{\left(x \right)} - \sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} \cot^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)}}{\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\cot{\left(x \right)} - 1\right) \left(\cot{\left(x \right)} + 1\right) \tan{\left(x \right)}}$$

-(-sin(x)^2 + cot(x)^2*sin(x)^2 + sin(x)^2*tan(x) + cos(x)*sin(x) + cos(x)^2*cot(x)^2*tan(x) - cot(x)^2*cos(x)*sin(x) - 2*cos(x)*sin(x)*tan(x))/((1 + cot(x))*(-1 + cot(x))*(-sin(x) + cos(x))*tan(x))

Unión de expresiones racionales [src]

/                    2      2    /       2   \\          /       2   \                          
\- (-cos(x) + sin(x))  + cos (x)*\1 - cot (x)//*tan(x) + \1 - cot (x)/*(-cos(x) + sin(x))*sin(x)
------------------------------------------------------------------------------------------------
                            /       2   \                                                       
                            \1 - cot (x)/*(-cos(x) + sin(x))*tan(x)

$$\frac{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} + \left(\left(1 - \cot^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} - \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}\right) \tan{\left(x \right)}}{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \tan{\left(x \right)}}$$

((-(-cos(x) + sin(x))^2 + cos(x)^2*(1 - cot(x)^2))*tan(x) + (1 - cot(x)^2)*(-cos(x) + sin(x))*sin(x))/((1 - cot(x)^2)*(-cos(x) + sin(x))*tan(x))

Abrimos la expresión [src]

                     2                              
   cos(x)         cos (x)       sin(x)      sin(x)  
----------- + --------------- + ------ - -----------
       2      sin(x) - cos(x)   tan(x)          2   
1 - cot (x)                              1 - cot (x)

$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}} + \frac{\cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$

cos(x)/(1 - cot(x)^2) + cos(x)^2/(sin(x) - cos(x)) + sin(x)/tan(x) - sin(x)/(1 - cot(x)^2)

Compilar la expresión [src]

       2                                    
    cos (x)        sin(x)   -cos(x) + sin(x)
---------------- + ------ - ----------------
-cos(x) + sin(x)   tan(x)            2      
                              1 - cot (x)

$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$

cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x) - (-cos(x) + sin(x))/(1 - cot(x)^2)

Respuesta numérica [src]

cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x) - (-cos(x) + sin(x))/(1.0 - cot(x)^2)

cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x) - (-cos(x) + sin(x))/(1.0 - cot(x)^2)

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¿Cómo vas a descomponer esta (cos^2x)/(sinx-cosx)-((sinx-cosx)/(1-ctg^2x))+sinx/tgx expresión en fracciones?

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