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-((-1+x^2/(1+x^2))/sqrt(1+x^2)+(1+x/sqrt(1+x^2))^2/(x+sqrt(1+x^2)))/(x+sqrt(1+x^2))
((z-1)*((z*f*r*f)/(1+(z-1)*c*f)))/(z*r)
y+y/x-y+1/(x^2)-x
y/(y+3)^2-y/(y^2)-9
Factorizar el polinomio:
z^2+2*z+26
z^2-169/196
y+y^2/2
y*y/x-x^2+x*y/x-y^2
Descomponer al cuadrado:
y^4-y^2-13
y^4-9*y^2+5
-y^4-9*y^2-4
-y^4+y^2+1
Expresiones idénticas
tgx/(uno -(tgx)^ dos)+ctgx/(uno +(ctgx)^ dos)
tgx dividir por (1 menos (tgx) al cuadrado ) más ctgx dividir por (1 más (ctgx) al cuadrado )
tgx dividir por (uno menos (tgx) en el grado dos) más ctgx dividir por (uno más (ctgx) en el grado dos)
tgx/(1-(tgx)2)+ctgx/(1+(ctgx)2)
tgx/1-tgx2+ctgx/1+ctgx2
tgx/(1-(tgx)²)+ctgx/(1+(ctgx)²)
tgx/(1-(tgx) en el grado 2)+ctgx/(1+(ctgx) en el grado 2)
tgx/1-tgx^2+ctgx/1+ctgx^2
tgx dividir por (1-(tgx)^2)+ctgx dividir por (1+(ctgx)^2)
Expresiones semejantes
tgx/(1-(tgx)^2)-ctgx/(1+(ctgx)^2)
tgx/(1-(tgx)^2)+ctgx/(1-(ctgx)^2)
tgx/(1+(tgx)^2)+ctgx/(1+(ctgx)^2)

Simplificación de expresiones/ Descomposición en fracciones simples/ tgx/(1-(tgx)^2)+ctgx/(1+(ctgx)^2)

¿Cómo vas a descomponer esta tgx/(1-(tgx)^2)+ctgx/(1+(ctgx)^2) expresión en fracciones?

Solución

Ha introducido [src]

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

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

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

Simplificación general [src]

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

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

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

Respuesta numérica [src]

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

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

Denominador racional [src]

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

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

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

Denominador común [src]

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

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

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

Combinatoria [src]

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

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

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

Unión de expresiones racionales [src]

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

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

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

Potencias [src]

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

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

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

Parte trigonométrica [src]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                2            
sin(2*x)   2*sin (x)*csc(2*x)
-------- + ------------------
   2                 2       
              1 - tan (x)

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

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

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

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

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

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

\frac{\sin{\left(2 x \right)}}{2} + \frac{\tan{\left(2 x \right)}}{2}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1/(2*csc(2*x)) + 2*csc(2*x)/((1 - csc(pi/2 - x)^2/csc(x)^2)*csc(x)^2)

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

¿Cómo vas a descomponer esta tgx/(1-(tgx)^2)+ctgx/(1+(ctgx)^2) expresión en fracciones?

Solución