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¿cómo vas a descomponer esta expresión en fracciones?:
(4*a^2-4*a+1)/(6*a^2-a-1)
(4*a+3*b)/(a+2*b)
x^8/(x-1)
x^42*x^42/((x^30*x^12))
Factorizar el polinomio:
x-y*x^3/3
y^2+1-10*y+24
y^2-12*x+x^2
x*y^2-x*z-y^3+y*z-y^2*z+z^2
Descomponer al cuadrado:
y^4-3*y^2-8
-y^4+3*y^2+6
-y^4+3*y^2+8
-y^4+3*y^2-4
Expresiones idénticas
sin(cuatro *a)/(cos(cuatro *a)-sin(cuatro *a))
seno de (4 multiplicar por a) dividir por ( coseno de (4 multiplicar por a) menos seno de (4 multiplicar por a))
seno de (cuatro multiplicar por a) dividir por ( coseno de (cuatro multiplicar por a) menos seno de (cuatro multiplicar por a))
sin(4a)/(cos(4a)-sin(4a))
sin4a/cos4a-sin4a
sin(4*a) dividir por (cos(4*a)-sin(4*a))
Expresiones semejantes
sin(4*a)/(cos(4*a)+sin(4*a))
Expresiones con funciones
Seno sin
sin((a+1/2)*x)/(2*(a+1/2))+sin((1/2-a)*x)/(2*(1/2-a))
sin(a)^(2)/(1+tan(a)^(2))+cos(a)^(2)/(1+cot(a)^(2))
sin(6*x)/((2*sin(3*x)))+2*sin(33/2)^2*x-sin(6)^2*x-cos(6)^2*x
sin^5/(cos^5+sin^5)
sin(4*x)/((cot(5*pi/4+2*x)*(1-sin(4*x))))
Seno sin
sin((a+1/2)*x)/(2*(a+1/2))+sin((1/2-a)*x)/(2*(1/2-a))
sin(a)^(2)/(1+tan(a)^(2))+cos(a)^(2)/(1+cot(a)^(2))
sin(6*x)/((2*sin(3*x)))+2*sin(33/2)^2*x-sin(6)^2*x-cos(6)^2*x
sin^5/(cos^5+sin^5)
sin(4*x)/((cot(5*pi/4+2*x)*(1-sin(4*x))))

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(4*a)/(cos(4*a)-sin(4*a))

¿Cómo vas a descomponer esta sin(4a)/(cos(4a)-sin(4*a)) expresión en fracciones?

Solución

Ha introducido [src]

      sin(4*a)     
-------------------
cos(4*a) - sin(4*a)

\frac{\sin{\left(4 a \right)}}{- \sin{\left(4 a \right)} + \cos{\left(4 a \right)}}

sin(4*a)/(cos(4*a) - sin(4*a))

Respuesta numérica [src]

sin(4*a)/(-sin(4*a) + cos(4*a))

sin(4*a)/(-sin(4*a) + cos(4*a))

Potencias [src]

              /   -4*I*a    4*I*a\           
           -I*\- e       + e     /           
---------------------------------------------
  / -4*I*a    4*I*a     /   -4*I*a    4*I*a\\
  |e         e        I*\- e       + e     /|
2*|------- + ------ + ----------------------|
  \   2        2                2           /

- \frac{i \left(e^{4 i a} - e^{- 4 i a}\right)}{2 \left(\frac{i \left(e^{4 i a} - e^{- 4 i a}\right)}{2} + \frac{e^{4 i a}}{2} + \frac{e^{- 4 i a}}{2}\right)}

-i*(-exp(-4*i*a) + exp(4*i*a))/(2*(exp(-4*i*a)/2 + exp(4*i*a)/2 + i*(-exp(-4*i*a) + exp(4*i*a))/2))

Abrimos la expresión [src]

                              3                                                                                                  
                         8*sin (a)*cos(a)                                                 4*cos(a)*sin(a)                        
- -------------------------------------------------------------- + --------------------------------------------------------------
           2           4                             3                      2           4                             3          
  1 - 8*cos (a) + 8*cos (a) - 4*cos(a)*sin(a) + 8*sin (a)*cos(a)   1 - 8*cos (a) + 8*cos (a) - 4*cos(a)*sin(a) + 8*sin (a)*cos(a)

- \frac{8 \sin^{3}{\left(a \right)} \cos{\left(a \right)}}{8 \sin^{3}{\left(a \right)} \cos{\left(a \right)} - 4 \sin{\left(a \right)} \cos{\left(a \right)} + 8 \cos^{4}{\left(a \right)} - 8 \cos^{2}{\left(a \right)} + 1} + \frac{4 \sin{\left(a \right)} \cos{\left(a \right)}}{8 \sin^{3}{\left(a \right)} \cos{\left(a \right)} - 4 \sin{\left(a \right)} \cos{\left(a \right)} + 8 \cos^{4}{\left(a \right)} - 8 \cos^{2}{\left(a \right)} + 1}

-8*sin(a)^3*cos(a)/(1 - 8*cos(a)^2 + 8*cos(a)^4 - 4*cos(a)*sin(a) + 8*sin(a)^3*cos(a)) + 4*cos(a)*sin(a)/(1 - 8*cos(a)^2 + 8*cos(a)^4 - 4*cos(a)*sin(a) + 8*sin(a)^3*cos(a))

Parte trigonométrica [src]

                   2*tan(2*a)                  
-----------------------------------------------
                /       2                     \
/       2     \ |1 - tan (2*a)     2*tan(2*a) |
\1 + tan (2*a)/*|------------- - -------------|
                |       2               2     |
                \1 + tan (2*a)   1 + tan (2*a)/

\frac{2 \tan{\left(2 a \right)}}{\left(\frac{1 - \tan^{2}{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1} - \frac{2 \tan{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1}\right) \left(\tan^{2}{\left(2 a \right)} + 1\right)}

         /      pi\       
      cos|4*a - --|       
         \      2 /       
--------------------------
     /      pi\           
- cos|4*a - --| + cos(4*a)
     \      2 /

\frac{\cos{\left(4 a - \frac{\pi}{2} \right)}}{\cos{\left(4 a \right)} - \cos{\left(4 a - \frac{\pi}{2} \right)}}

                2                         
           2*sin (2*a)*cot(2*a)           
------------------------------------------
                 2/      pi\    /      pi\
-sin(4*a) + 2*sin |2*a + --|*cot|2*a + --|
                  \      4 /    \      4 /

\frac{2 \sin^{2}{\left(2 a \right)} \cot{\left(2 a \right)}}{- \sin{\left(4 a \right)} + 2 \sin^{2}{\left(2 a + \frac{\pi}{4} \right)} \cot{\left(2 a + \frac{\pi}{4} \right)}}

                            2                            
---------------------------------------------------------
/                       2        \                       
|                    csc (2*a)   |                       
|             -1 + --------------|                       
|                     2/pi      \|                       
|                  csc |-- - 2*a||                       
|     1                \2       /|             /pi      \
|- -------- + -------------------|*csc(2*a)*csc|-- - 2*a|
|  csc(4*a)           2          |             \2       /
\                  csc (2*a)     /

\frac{2}{\left(\frac{\frac{\csc^{2}{\left(2 a \right)}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}} - 1}{\csc^{2}{\left(2 a \right)}} - \frac{1}{\csc{\left(4 a \right)}}\right) \csc{\left(2 a \right)} \csc{\left(- 2 a + \frac{\pi}{2} \right)}}

              2                       
         2*sin (2*a)*cot(2*a)         
--------------------------------------
               2      /        2     \
-sin(4*a) + sin (2*a)*\-1 + cot (2*a)/

\frac{2 \sin^{2}{\left(2 a \right)} \cot{\left(2 a \right)}}{\left(\cot^{2}{\left(2 a \right)} - 1\right) \sin^{2}{\left(2 a \right)} - \sin{\left(4 a \right)}}

              2                       
         2*sin (2*a)*cot(2*a)         
--------------------------------------
          2                           
-1 + 2*cos (2*a) + cos(4*a)           
--------------------------- - sin(4*a)
             2

\frac{2 \sin^{2}{\left(2 a \right)} \cot{\left(2 a \right)}}{\frac{2 \cos^{2}{\left(2 a \right)} + \cos{\left(4 a \right)} - 1}{2} - \sin{\left(4 a \right)}}

                   1                    
----------------------------------------
/   1             1      \    /      pi\
|-------- - -------------|*sec|4*a - --|
|sec(4*a)      /      pi\|    \      2 /
|           sec|4*a - --||              
\              \      2 //

\frac{1}{\left(- \frac{1}{\sec{\left(4 a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(4 a \right)}}\right) \sec{\left(4 a - \frac{\pi}{2} \right)}}

                             /      pi\               
               2*cos(2*a)*cos|2*a - --|               
                             \      2 /               
------------------------------------------------------
                                 /          2        \
     /      pi\      2/      pi\ |       cos (2*a)   |
- cos|4*a - --| + cos |2*a - --|*|-1 + --------------|
     \      2 /       \      2 / |        2/      pi\|
                                 |     cos |2*a - --||
                                 \         \      2 //

\frac{2 \cos{\left(2 a \right)} \cos{\left(2 a - \frac{\pi}{2} \right)}}{\left(\frac{\cos^{2}{\left(2 a \right)}}{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(2 a - \frac{\pi}{2} \right)} - \cos{\left(4 a - \frac{\pi}{2} \right)}}

         sin(4*a)        
-------------------------
               /pi      \
-sin(4*a) + sin|-- + 4*a|
               \2       /

\frac{\sin{\left(4 a \right)}}{- \sin{\left(4 a \right)} + \sin{\left(4 a + \frac{\pi}{2} \right)}}

                         2                         
           /        2   \     4                    
         2*\-1 + cot (a)/ *sin (a)*tan(2*a)        
---------------------------------------------------
                          2                        
            /        2   \     4    /       2     \
-sin(4*a) + \-1 + cot (a)/ *sin (a)*\1 - tan (2*a)/

\frac{2 \left(\cot^{2}{\left(a \right)} - 1\right)^{2} \sin^{4}{\left(a \right)} \tan{\left(2 a \right)}}{\left(1 - \tan^{2}{\left(2 a \right)}\right) \left(\cot^{2}{\left(a \right)} - 1\right)^{2} \sin^{4}{\left(a \right)} - \sin{\left(4 a \right)}}

                      2*tan(2*a)                      
------------------------------------------------------
                /                        /      pi\  \
                |                   2*tan|2*a + --|  |
/       2     \ |    2*tan(2*a)          \      4 /  |
\1 + tan (2*a)/*|- ------------- + ------------------|
                |         2               2/      pi\|
                |  1 + tan (2*a)   1 + tan |2*a + --||
                \                          \      4 //

\frac{2 \tan{\left(2 a \right)}}{\left(\frac{2 \tan{\left(2 a + \frac{\pi}{4} \right)}}{\tan^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1} - \frac{2 \tan{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1}\right) \left(\tan^{2}{\left(2 a \right)} + 1\right)}

         2*cos(2*a)*sin(2*a)          
--------------------------------------
               2      /         1    \
-sin(4*a) + sin (2*a)*|-1 + ---------|
                      |        2     |
                      \     tan (2*a)/

\frac{2 \sin{\left(2 a \right)} \cos{\left(2 a \right)}}{\left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} - \sin{\left(4 a \right)}}

              2                       
         2*cos (2*a)*tan(2*a)         
--------------------------------------
          2                           
-1 + 2*cos (2*a) + cos(4*a)           
--------------------------- - sin(4*a)
             2

\frac{2 \cos^{2}{\left(2 a \right)} \tan{\left(2 a \right)}}{\frac{2 \cos^{2}{\left(2 a \right)} + \cos{\left(4 a \right)} - 1}{2} - \sin{\left(4 a \right)}}

                      2*cot(2*a)                      
------------------------------------------------------
                /                        /      pi\  \
                |                   2*tan|2*a + --|  |
/       2     \ |    2*cot(2*a)          \      4 /  |
\1 + cot (2*a)/*|- ------------- + ------------------|
                |         2               2/      pi\|
                |  1 + cot (2*a)   1 + tan |2*a + --||
                \                          \      4 //

\frac{2 \cot{\left(2 a \right)}}{\left(- \frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} + \frac{2 \tan{\left(2 a + \frac{\pi}{4} \right)}}{\tan^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1}\right) \left(\cot^{2}{\left(2 a \right)} + 1\right)}

              1               
------------------------------
/   1          1    \         
|-------- - --------|*csc(4*a)
\sec(4*a)   csc(4*a)/

\frac{1}{\left(\frac{1}{\sec{\left(4 a \right)}} - \frac{1}{\csc{\left(4 a \right)}}\right) \csc{\left(4 a \right)}}

                      2*cot(2*a)                      
------------------------------------------------------
                /                        /      pi\  \
                |                   2*cot|2*a + --|  |
/       2     \ |    2*cot(2*a)          \      4 /  |
\1 + cot (2*a)/*|- ------------- + ------------------|
                |         2               2/      pi\|
                |  1 + cot (2*a)   1 + cot |2*a + --||
                \                          \      4 //

\frac{2 \cot{\left(2 a \right)}}{\left(\frac{2 \cot{\left(2 a + \frac{\pi}{4} \right)}}{\cot^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1} - \frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1}\right) \left(\cot^{2}{\left(2 a \right)} + 1\right)}

                           2                            
--------------------------------------------------------
/                    2/pi      \\                       
|                 csc |-- - 2*a||                       
|                     \2       /|                       
|             1 - --------------|                       
|                      2        |                       
|     1             csc (2*a)   |             /pi      \
|- -------- + ------------------|*csc(2*a)*csc|-- - 2*a|
|  csc(4*a)        2/pi      \  |             \2       /
|               csc |-- - 2*a|  |                       
\                   \2       /  /

\frac{2}{\left(\frac{1 - \frac{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 a \right)}}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(4 a \right)}}\right) \csc{\left(2 a \right)} \csc{\left(- 2 a + \frac{\pi}{2} \right)}}

                   2         2                    
              4*cos (2*a)*sin (2*a)               
--------------------------------------------------
/                      /         4     \\         
|               2      |    4*sin (2*a)||         
|-sin(4*a) + cos (2*a)*|1 - -----------||*sin(4*a)
|                      |        2      ||         
\                      \     sin (4*a) //

\frac{4 \sin^{2}{\left(2 a \right)} \cos^{2}{\left(2 a \right)}}{\left(\left(- \frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1\right) \cos^{2}{\left(2 a \right)} - \sin{\left(4 a \right)}\right) \sin{\left(4 a \right)}}

               2       4                      
          8*cot (a)*sin (a)*cot(2*a)          
----------------------------------------------
                 2       4    /        2     \
-sin(4*a) + 4*cot (a)*sin (a)*\-1 + cot (2*a)/

\frac{8 \sin^{4}{\left(a \right)} \cot^{2}{\left(a \right)} \cot{\left(2 a \right)}}{4 \left(\cot^{2}{\left(2 a \right)} - 1\right) \sin^{4}{\left(a \right)} \cot^{2}{\left(a \right)} - \sin{\left(4 a \right)}}

                                   2                                  
                              8*tan (a)                               
----------------------------------------------------------------------
               /                       2    /         1    \\         
               |                  4*tan (a)*|-1 + ---------||         
             2 |                            |        2     ||         
/       2   \  |    2*tan(2*a)              \     tan (2*a)/|         
\1 + tan (a)/ *|- ------------- + --------------------------|*tan(2*a)
               |         2                           2      |         
               |  1 + tan (2*a)         /       2   \       |         
               \                        \1 + tan (a)/       /

\frac{8 \tan^{2}{\left(a \right)}}{\left(\frac{4 \left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \tan^{2}{\left(a \right)}}{\left(\tan^{2}{\left(a \right)} + 1\right)^{2}} - \frac{2 \tan{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1}\right) \left(\tan^{2}{\left(a \right)} + 1\right)^{2} \tan{\left(2 a \right)}}

                   2*cot(2*a)                   
------------------------------------------------
                /        2                     \
/       2     \ |-1 + cot (2*a)     2*cot(2*a) |
\1 + cot (2*a)/*|-------------- - -------------|
                |       2                2     |
                \1 + cot (2*a)    1 + cot (2*a)/

\frac{2 \cot{\left(2 a \right)}}{\left(\frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1} - \frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1}\right) \left(\cot^{2}{\left(2 a \right)} + 1\right)}

   2*cos(2*a)*sin(2*a)   
-------------------------
                   2     
            1 - tan (2*a)
-sin(4*a) + -------------
                 2       
              sec (2*a)

\frac{2 \sin{\left(2 a \right)} \cos{\left(2 a \right)}}{\frac{1 - \tan^{2}{\left(2 a \right)}}{\sec^{2}{\left(2 a \right)}} - \sin{\left(4 a \right)}}

                                             2                             
                               /        2   \                              
                             2*\-1 + cot (a)/                              
---------------------------------------------------------------------------
               /                                2                \         
               |                  /        2   \  /        1    \|         
               |                  \-1 + cot (a)/ *|1 - ---------||         
             2 |                                  |       2     ||         
/       2   \  |    2*cot(2*a)                    \    cot (2*a)/|         
\1 + cot (a)/ *|- ------------- + -------------------------------|*cot(2*a)
               |         2                              2        |         
               |  1 + cot (2*a)            /       2   \         |         
               \                           \1 + cot (a)/         /

\frac{2 \left(\cot^{2}{\left(a \right)} - 1\right)^{2}}{\left(\frac{\left(1 - \frac{1}{\cot^{2}{\left(2 a \right)}}\right) \left(\cot^{2}{\left(a \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}} - \frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1}\right) \left(\cot^{2}{\left(a \right)} + 1\right)^{2} \cot{\left(2 a \right)}}

                              2                              
-------------------------------------------------------------
/                           2        \                       
|                        sec (2*a)   |                       
|                  1 - --------------|                       
|                         2/      pi\|                       
|                      sec |2*a - --||                       
|        1                 \      2 /|             /      pi\
|- ------------- + ------------------|*sec(2*a)*sec|2*a - --|
|     /      pi\          2          |             \      2 /
|  sec|4*a - --|       sec (2*a)     |                       
\     \      2 /                     /

\frac{2}{\left(\frac{- \frac{\sec^{2}{\left(2 a \right)}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1}{\sec^{2}{\left(2 a \right)}} - \frac{1}{\sec{\left(4 a - \frac{\pi}{2} \right)}}\right) \sec{\left(2 a \right)} \sec{\left(2 a - \frac{\pi}{2} \right)}}

      sin(4*a)     
-------------------
   1               
-------- - sin(4*a)
sec(4*a)

\frac{\sin{\left(4 a \right)}}{- \sin{\left(4 a \right)} + \frac{1}{\sec{\left(4 a \right)}}}

                    2         2/pi      \              
               4*sin (2*a)*sin |-- + 2*a|              
                               \2       /              
-------------------------------------------------------
/                           /         4     \\         
|               2/pi      \ |    4*sin (2*a)||         
|-sin(4*a) + sin |-- + 2*a|*|1 - -----------||*sin(4*a)
|                \2       / |        2      ||         
\                           \     sin (4*a) //

\frac{4 \sin^{2}{\left(2 a \right)} \sin^{2}{\left(2 a + \frac{\pi}{2} \right)}}{\left(\left(- \frac{4 \sin^{4}{\left(2 a \right)}}{\sin^{2}{\left(4 a \right)}} + 1\right) \sin^{2}{\left(2 a + \frac{\pi}{2} \right)} - \sin{\left(4 a \right)}\right) \sin{\left(4 a \right)}}

                           2                                 
                      8*cot (a)*cot(2*a)                     
-------------------------------------------------------------
             2 /                       2    /        2     \\
/       2   \  |    2*cot(2*a)    4*cot (a)*\-1 + cot (2*a)/|
\1 + cot (a)/ *|- ------------- + --------------------------|
               |         2                           2      |
               |  1 + cot (2*a)         /       2   \       |
               \                        \1 + cot (a)/       /

\frac{8 \cot^{2}{\left(a \right)} \cot{\left(2 a \right)}}{\left(- \frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} + \frac{4 \left(\cot^{2}{\left(2 a \right)} - 1\right) \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(a \right)} + 1\right)^{2}}

                 1                 
-----------------------------------
/      1            1    \         
|------------- - --------|*csc(4*a)
|   /pi      \   csc(4*a)|         
|csc|-- - 4*a|           |         
\   \2       /           /

\frac{1}{\left(\frac{1}{\csc{\left(- 4 a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(4 a \right)}}\right) \csc{\left(4 a \right)}}

        sin(4*a)        
------------------------
      1                 
------------- - sin(4*a)
   /pi      \           
csc|-- - 4*a|           
   \2       /

\frac{\sin{\left(4 a \right)}}{- \sin{\left(4 a \right)} + \frac{1}{\csc{\left(- 4 a + \frac{\pi}{2} \right)}}}

                              2                               
--------------------------------------------------------------
/                          2/      pi\\                       
|                       sec |2*a - --||                       
|                           \      2 /|                       
|                  -1 + --------------|                       
|                            2        |                       
|        1                sec (2*a)   |             /      pi\
|- ------------- + -------------------|*sec(2*a)*sec|2*a - --|
|     /      pi\         2/      pi\  |             \      2 /
|  sec|4*a - --|      sec |2*a - --|  |                       
\     \      2 /          \      2 /  /

\frac{2}{\left(\frac{-1 + \frac{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 a \right)}}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(4 a - \frac{\pi}{2} \right)}}\right) \sec{\left(2 a \right)} \sec{\left(2 a - \frac{\pi}{2} \right)}}

         2*cos(2*a)*sin(2*a)         
-------------------------------------
               2      /       2     \
-sin(4*a) + cos (2*a)*\1 - tan (2*a)/

\frac{2 \sin{\left(2 a \right)} \cos{\left(2 a \right)}}{\left(1 - \tan^{2}{\left(2 a \right)}\right) \cos^{2}{\left(2 a \right)} - \sin{\left(4 a \right)}}

              2                      
         2*cos (2*a)*tan(2*a)        
-------------------------------------
               2      /       2     \
-sin(4*a) + cos (2*a)*\1 - tan (2*a)/

\frac{2 \cos^{2}{\left(2 a \right)} \tan{\left(2 a \right)}}{\left(1 - \tan^{2}{\left(2 a \right)}\right) \cos^{2}{\left(2 a \right)} - \sin{\left(4 a \right)}}

                                          sin(4*a)                                          
--------------------------------------------------------------------------------------------
                             ___    /      pi\     ___    /      pi\       ___    /      pi\
-2*sin(2*a) + 4*cos(2*a) + \/ 2 *cos|4*a + --| - \/ 2 *sin|2*a + --| - 3*\/ 2 *cos|2*a + --|
                                    \      4 /            \      4 /              \      4 /

\frac{\sin{\left(4 a \right)}}{- 2 \sin{\left(2 a \right)} - \sqrt{2} \sin{\left(2 a + \frac{\pi}{4} \right)} + 4 \cos{\left(2 a \right)} - 3 \sqrt{2} \cos{\left(2 a + \frac{\pi}{4} \right)} + \sqrt{2} \cos{\left(4 a + \frac{\pi}{4} \right)}}

   2*cos(2*a)*sin(2*a)    
--------------------------
                     1    
            -1 + ---------
                    2     
                 tan (2*a)
-sin(4*a) + --------------
                 2        
              csc (2*a)

\frac{2 \sin{\left(2 a \right)} \cos{\left(2 a \right)}}{\frac{-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}}{\csc^{2}{\left(2 a \right)}} - \sin{\left(4 a \right)}}

                                   2                             
                      /       2   \                              
                    2*\1 - tan (a)/ *tan(2*a)                    
-----------------------------------------------------------------
               /                               2                \
             2 |                  /       2   \  /       2     \|
/       2   \  |    2*tan(2*a)    \1 - tan (a)/ *\1 - tan (2*a)/|
\1 + tan (a)/ *|- ------------- + ------------------------------|
               |         2                             2        |
               |  1 + tan (2*a)           /       2   \         |
               \                          \1 + tan (a)/         /

\frac{2 \left(1 - \tan^{2}{\left(a \right)}\right)^{2} \tan{\left(2 a \right)}}{\left(\frac{\left(1 - \tan^{2}{\left(a \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 a \right)}\right)}{\left(\tan^{2}{\left(a \right)} + 1\right)^{2}} - \frac{2 \tan{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1}\right) \left(\tan^{2}{\left(a \right)} + 1\right)^{2}}

                       2                          
          /       2   \     4                     
        2*\1 - tan (a)/ *cos (a)*tan(2*a)         
--------------------------------------------------
                         2                        
            /       2   \     4    /       2     \
-sin(4*a) + \1 - tan (a)/ *cos (a)*\1 - tan (2*a)/

\frac{2 \left(1 - \tan^{2}{\left(a \right)}\right)^{2} \cos^{4}{\left(a \right)} \tan{\left(2 a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 a \right)}\right) \cos^{4}{\left(a \right)} - \sin{\left(4 a \right)}}

                          /      pi\            
            2*cos(2*a)*cos|2*a - --|            
                          \      2 /            
------------------------------------------------
                            /       2/      pi\\
                            |    cos |2*a - --||
     /      pi\      2      |        \      2 /|
- cos|4*a - --| + cos (2*a)*|1 - --------------|
     \      2 /             |         2        |
                            \      cos (2*a)   /

\frac{2 \cos{\left(2 a \right)} \cos{\left(2 a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 a \right)}}\right) \cos^{2}{\left(2 a \right)} - \cos{\left(4 a - \frac{\pi}{2} \right)}}

                sin(4*a)                
----------------------------------------
                      /         2      \
               2      |      sin (4*a) |
-sin(4*a) + sin (2*a)*|-1 + -----------|
                      |          4     |
                      \     4*sin (2*a)/

\frac{\sin{\left(4 a \right)}}{\left(-1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} - \sin{\left(4 a \right)}}

sin(4*a)/(-sin(4*a) + sin(2*a)^2*(-1 + sin(4*a)^2/(4*sin(2*a)^4)))

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¿Cómo vas a descomponer esta sin(4*a)/(cos(4*a)-sin(4*a)) expresión en fracciones?

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¿Cómo vas a descomponer esta sin(4a)/(cos(4a)-sin(4*a)) expresión en fracciones?