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(y-x)/(y/x-x/y)
-1/x+3/(x^2+2)
(a^2+4ab+b^2)/(a+b)^2
(y-x/y*(x+y))*(-x*y/(x^3-x*y^2))
Factorizar el polinomio:
y^2+x*y+x^2+2*x+2*y
y^2-5*x^2/4-11/2
y^2+2*y*w+w^2
y^2-x*y+3*x-y-6
Descomponer al cuadrado:
-y^4+6*y^2+9
y^4-5*y^2-5
y^4-5*y^2+15
-y^4-4*y^2-8
Expresiones idénticas
cos^ dos (x)/(cos^ dos (x)- uno)
coseno de al cuadrado (x) dividir por ( coseno de al cuadrado (x) menos 1)
coseno de en el grado dos (x) dividir por ( coseno de en el grado dos (x) menos uno)
cos2(x)/(cos2(x)-1)
cos2x/cos2x-1
cos²(x)/(cos²(x)-1)
cos en el grado 2(x)/(cos en el grado 2(x)-1)
cos^2x/cos^2x-1
cos^2(x) dividir por (cos^2(x)-1)
Expresiones semejantes
cos^2(x)/(cos^2(x)+1)
Expresiones con funciones
Coseno cos
cos^4x/(sinx(cos^5x+sin^5x))
cos(2*x)/((sin(2*x)*cos(x)))
cos2x-sin2x/(cos4x-sin4x+2sin^2(2x))
cos(2*x)^(1/x)*(-log(cos(2*x))/x^2-2*sin(2*x)/(x*cos(2*x)))
cos^2a/(2sin^2a-1)+sin^2a/(2cos^2a-1)
Coseno cos
cos^4x/(sinx(cos^5x+sin^5x))
cos(2*x)/((sin(2*x)*cos(x)))
cos2x-sin2x/(cos4x-sin4x+2sin^2(2x))
cos(2*x)^(1/x)*(-log(cos(2*x))/x^2-2*sin(2*x)/(x*cos(2*x)))
cos^2a/(2sin^2a-1)+sin^2a/(2cos^2a-1)

Simplificación de expresiones/ Descomposición en fracciones simples/ cos^2(x)/(cos^2(x)-1)

¿Cómo vas a descomponer esta cos^2(x)/(cos^2(x)-1) expresión en fracciones?

Solución

Ha introducido [src]

     2     
  cos (x)  
-----------
   2       
cos (x) - 1

\frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}

cos(x)^2/(cos(x)^2 - 1)

Simplificación general [src]

  -1   
-------
   2   
tan (x)

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

-1/tan(x)^2

Descomposición de una fracción [src]

1 + 1/(2*(-1 + cos(x))) - 1/(2*(1 + cos(x)))

1 - \frac{1}{2 \left(\cos{\left(x \right)} + 1\right)} + \frac{1}{2 \left(\cos{\left(x \right)} - 1\right)}

           1                1       
1 + --------------- - --------------
    2*(-1 + cos(x))   2*(1 + cos(x))

Respuesta numérica [src]

cos(x)^2/(-1.0 + cos(x)^2)

cos(x)^2/(-1.0 + cos(x)^2)

Denominador común [src]

         1      
1 + ------------
            2   
    -1 + cos (x)

1 + \frac{1}{\cos^{2}{\left(x \right)} - 1}

1 + 1/(-1 + cos(x)^2)

Potencias [src]

                2   
  / I*x    -I*x\    
  |e      e    |    
  |---- + -----|    
  \ 2       2  /    
--------------------
                   2
     / I*x    -I*x\ 
     |e      e    | 
-1 + |---- + -----| 
     \ 2       2  /

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

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

Combinatoria [src]

            2             
         cos (x)          
--------------------------
(1 + cos(x))*(-1 + cos(x))

\frac{\cos^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right) \left(\cos{\left(x \right)} + 1\right)}

cos(x)^2/((1 + cos(x))*(-1 + cos(x)))

Parte trigonométrica [src]

      2/    pi\  
   sin |x + --|  
       \    2 /  
-----------------
        2/    pi\
-1 + sin |x + --|
         \    2 /

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

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

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

              2              2               4 
 /       2/x\\  /       1   \  /        2/x\\  
-|1 + cot |-|| *|1 - -------| *|-1 + cot |-||  
 \        \2//  |       2/x\|  \         \4//  
                |    cot |-||                  
                \        \2//                  
-----------------------------------------------
                           4                   
              /       2/x\\     2/x\           
            4*|1 + cot |-|| *cot |-|           
              \        \4//      \2/

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

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

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

  -1   
-------
   2   
tan (x)

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

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

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

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

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

              2              2              4 
 /       2/x\\  /       2/x\\  /       2/x\\  
-|1 + tan |-|| *|1 - tan |-|| *|1 - tan |-||  
 \        \2//  \        \2//  \        \4//  
----------------------------------------------
                          4                   
             /       2/x\\     2/x\           
           4*|1 + tan |-|| *tan |-|           
             \        \4//      \2/

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

                   2              
 /         2/x\   \               
 |      sec |-|   |               
 |          \2/   |     2/    pi\ 
-|1 - ------------| *sec |x - --| 
 |       2/x   pi\|      \    2 / 
 |    sec |- - --||               
 \        \2   2 //               
----------------------------------
                4/x\              
             sec |-|              
                 \2/

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

          1           
----------------------
/        1   \    2   
|-1 + -------|*sec (x)
|        2   |        
\     sec (x)/

\frac{1}{\left(-1 + \frac{1}{\sec^{2}{\left(x \right)}}\right) \sec^{2}{\left(x \right)}}

    2      
-sin (2*x) 
-----------
      4    
 4*sin (x)

- \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}

               2                
 /        1   \     2       4/x\
-|-1 + -------| *csc (x)*sin |-|
 |        2/x\|              \2/
 |     tan |-||                 
 \         \2//

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

                    2              
 /        2/x   pi\\               
 |     sec |- - --||               
 |         \2   2 /|     2/    pi\ 
-|-1 + ------------| *sec |x - --| 
 |          2/x\   |      \    2 / 
 |       sec |-|   |               
 \           \2/   /               
-----------------------------------
               4/x   pi\           
            sec |- - --|           
                \2   2 /

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

                   2         
 /       2/x   pi\\          
 |    cos |- - --||          
 |        \2   2 /|     4/x\ 
-|1 - ------------| *cos |-| 
 |         2/x\   |      \2/ 
 |      cos |-|   |          
 \          \2/   /          
-----------------------------
            2/    pi\        
         cos |x - --|        
             \    2 /

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

                    2              
 /          2/x\   \               
 |       cos |-|   |               
 |           \2/   |     4/x   pi\ 
-|-1 + ------------| *cos |- - --| 
 |        2/x   pi\|      \2   2 / 
 |     cos |- - --||               
 \         \2   2 //               
-----------------------------------
               2/    pi\           
            cos |x - --|           
                \    2 /

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

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

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

     2      
 -csc (x)   
------------
   2/pi    \
csc |-- - x|
    \2     /

- \frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}

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

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

               1                
--------------------------------
/          1      \    2/pi    \
|-1 + ------------|*csc |-- - x|
|        2/pi    \|     \2     /
|     csc |-- - x||             
\         \2     //

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

                        2           
           /       2/x\\            
           |1 - tan |-||            
           \        \2//            
------------------------------------
               /                  2\
               |     /       2/x\\ |
             2 |     |1 - tan |-|| |
/       2/x\\  |     \        \2// |
|1 + tan |-|| *|-1 + --------------|
\        \2//  |                  2|
               |     /       2/x\\ |
               |     |1 + tan |-|| |
               \     \        \2// /

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

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

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

    2   
-cot (x)

- \cot^{2}{\left(x \right)}

                         2           
           /        2/x\\            
           |-1 + cot |-||            
           \         \2//            
-------------------------------------
               /                   2\
               |     /        2/x\\ |
             2 |     |-1 + cot |-|| |
/       2/x\\  |     \         \2// |
|1 + cot |-|| *|-1 + ---------------|
\        \2//  |                   2|
               |      /       2/x\\ |
               |      |1 + cot |-|| |
               \      \        \2// /

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

                2               2        
   /       2/x\\  /        2/x\\     4/x\
-4*|1 + cot |-|| *|-1 + cot |-|| *cot |-|
   \        \2//  \         \2//      \4/
-----------------------------------------
                       4                 
          /       2/x\\     2/x\         
          |1 + cot |-|| *cot |-|         
          \        \4//      \2/

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

     2      
 -cos (x)   
------------
   2/    pi\
cos |x - --|
    \    2 /

- \frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}

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

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

              2              4         
 /       2/x\\  /       2/x\\     8/x\ 
-|1 - tan |-|| *|1 - tan |-|| *cos |-| 
 \        \2//  \        \4//      \4/ 
---------------------------------------
                4/x\    2/x\           
           4*cos |-|*tan |-|           
                 \2/     \2/

- \frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \cos^{8}{\left(\frac{x}{4} \right)}}{4 \cos^{4}{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}

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

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

              2               4                 
 /       2/x\\  /        2/x\\     8/x\    2/x\ 
-|1 - tan |-|| *|-1 + cot |-|| *sin |-|*tan |-| 
 \        \2//  \         \4//      \4/     \2/ 
------------------------------------------------
                        4/x\                    
                   4*sin |-|                    
                         \2/

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

                2               2        
   /       2/x\\  /        1   \     4/x\
-4*|1 + tan |-|| *|-1 + -------| *tan |-|
   \        \2//  |        2/x\|      \4/
                  |     tan |-||         
                  \         \2//         
-----------------------------------------
                       4                 
          /       2/x\\     2/x\         
          |1 + tan |-|| *tan |-|         
          \        \4//      \2/

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

        1           1    
1 - --------- - ---------
         2/x\        2/x\
    4*cos |-|   4*sin |-|
          \2/         \2/

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

       4/x\             
    sin |-|       2     
1       \2/    sin (x)  
- - ------- - ----------
2      2            4/x\
    sin (x)   16*sin |-|
                     \2/

- \frac{\sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{2} - \frac{\sin^{2}{\left(x \right)}}{16 \sin^{4}{\left(\frac{x}{2} \right)}}

    2/    pi\ 
-sec |x - --| 
     \    2 / 
--------------
      2       
   sec (x)

- \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}

-sec(x - pi/2)^2/sec(x)^2

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta cos^2(x)/(cos^2(x)-1) expresión en fracciones?

Solución