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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
cos(x)/(uno +tan(x))+(- uno -tan(x)^ dos)*sin(x)/(uno +tan(x))^ dos
coseno de (x) dividir por (1 más tangente de (x)) más ( menos 1 menos tangente de (x) al cuadrado ) multiplicar por seno de (x) dividir por (1 más tangente de (x)) al cuadrado
coseno de (x) dividir por (uno más tangente de (x)) más ( menos uno menos tangente de (x) en el grado dos) multiplicar por seno de (x) dividir por (uno más tangente de (x)) en el grado dos
cos(x)/(1+tan(x))+(-1-tan(x)2)*sin(x)/(1+tan(x))2
cosx/1+tanx+-1-tanx2*sinx/1+tanx2
cos(x)/(1+tan(x))+(-1-tan(x)²)*sin(x)/(1+tan(x))²
cos(x)/(1+tan(x))+(-1-tan(x) en el grado 2)*sin(x)/(1+tan(x)) en el grado 2
cos(x)/(1+tan(x))+(-1-tan(x)^2)sin(x)/(1+tan(x))^2
cos(x)/(1+tan(x))+(-1-tan(x)2)sin(x)/(1+tan(x))2
cosx/1+tanx+-1-tanx2sinx/1+tanx2
cosx/1+tanx+-1-tanx^2sinx/1+tanx^2
cos(x) dividir por (1+tan(x))+(-1-tan(x)^2)*sin(x) dividir por (1+tan(x))^2
Expresiones semejantes
cos(x)/(1+tan(x))+(1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos(x)/(1-tan(x))+(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos(x)/(1+tan(x))-(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos(x)/(1+tan(x))+(-1-tan(x)^2)*sin(x)/(1-tan(x))^2
cos(x)/(1+tan(x))+(-1+tan(x)^2)*sin(x)/(1+tan(x))^2
cosx/(1+tan(x))+(-1-tan(x)^2)*sinx/(1+tan(x))^2
Expresiones con funciones
Coseno cos
cos((7pi/24)+pi/8)/(√6*sin(pi/10+(3pi)/20))
cos(x)^(2/x)*(-2*log(cos(x))/x^2-2*sin(x)/(x*cos(x)))
cos(pi*x)*exp(x)/(1+pi^2)+pi*exp(x)*sin(pi*x)/(1+pi^2)
cos(-x)*cos(pi+x)/(sin(-x)*sin(pi/2+x))
cos(sqrt(x))/(2*sqrt(x))
Tangente tan
tan(x+pi/8)/2-1/(2*tan(x+pi/8))
tan(pi/8)/(1-tan^2(pi/8))
tan(x)/(2+2*tan(x)^2)+x/2
tan(x)+coscos(x)/(sin*sin(x)+1)
tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2)
Tangente tan
tan(x+pi/8)/2-1/(2*tan(x+pi/8))
tan(pi/8)/(1-tan^2(pi/8))
tan(x)/(2+2*tan(x)^2)+x/2
tan(x)+coscos(x)/(sin*sin(x)+1)
tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2)
Seno sin
sin(14*x)/((2*cos(7*x)))
sin(2*a)/((2*sin(a)))
sin(x)/(2*sqrt(cos(x)))-sin(sqrt(x))/(2*sqrt(x))
sinx/(tan((pi/4)-(x/2))*(1+sinx))
sinx/(((1+tgx/2)/(1-tgx/2))*(1+sinx))
Tangente tan
tan(x+pi/8)/2-1/(2*tan(x+pi/8))
tan(pi/8)/(1-tan^2(pi/8))
tan(x)/(2+2*tan(x)^2)+x/2
tan(x)+coscos(x)/(sin*sin(x)+1)
tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2)

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

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

Solución

Ha introducido [src]

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

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

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

Simplificación general [src]

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

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

(sqrt(2)*sin(x + pi/4) - sin(x)/cos(x)^2)/(1 + tan(x))^2

Unión de expresiones racionales [src]

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

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

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

Respuesta numérica [src]

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

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

Denominador común [src]

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

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

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

Combinatoria [src]

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

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

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

Denominador racional [src]

            2                       /        2   \       
(1 + tan(x)) *cos(x) + (1 + tan(x))*\-1 - tan (x)/*sin(x)
---------------------------------------------------------
                                  3                      
                      (1 + tan(x))

\frac{\left(\tan{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)} + \left(\tan{\left(x \right)} + 1\right) \left(- \tan^{2}{\left(x \right)} - 1\right) \sin{\left(x \right)}}{\left(\tan{\left(x \right)} + 1\right)^{3}}

((1 + tan(x))^2*cos(x) + (1 + tan(x))*(-1 - tan(x)^2)*sin(x))/(1 + tan(x))^3

Compilar la expresión [src]

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

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

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

Abrimos la expresión [src]

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

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

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

Potencias [src]

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

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

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

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

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

Parte trigonométrica [src]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                2          
  cos(x)     sec (x)*sin(x)
---------- - --------------
1 + tan(x)               2 
             (1 + tan(x))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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