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Descomponer al cuadrado:
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y^4-y^2-5
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cos^2a/1+sina
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Expresiones semejantes
cos^2a/(1-sina)
Expresiones con funciones
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cos(x-sin(x))/(4*x-pi)
cos((\pi)/(2)+a)cos(\pi-a)+sin((3\pi)/(2)+a)sin(\pi+a)
sina
sina/(sin^3a+3cos^3a)

Simplificación de expresiones/ Descomposición en fracciones simples/ cos^2a/(1+sina)

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

Solución

Ha introducido [src]

    2     
 cos (a)  
----------
1 + sin(a)

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

cos(a)^2/(1 + sin(a))

Simplificación general [src]

1 - sin(a)

$$1 - \sin{\left(a \right)}$$

1 - sin(a)

Respuesta numérica [src]

cos(a)^2/(1.0 + sin(a))

cos(a)^2/(1.0 + sin(a))

Potencias [src]

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

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

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

Parte trigonométrica [src]

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

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

                 2                
   /        1   \     8/a\    4/a\
16*|-1 + -------| *cos |-|*tan |-|
   |        2/a\|      \4/     \4/
   |     tan |-||                 
   \         \2//                 
----------------------------------
            1 + sin(a)

$$\frac{16 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cos^{8}{\left(\frac{a}{4} \right)} \tan^{4}{\left(\frac{a}{4} \right)}}{\sin{\left(a \right)} + 1}$$

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

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

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

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

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

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

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

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

                    2           
      /        2/a\\     4/a\   
   16*|-1 + cot |-|| *cot |-|   
      \         \2//      \4/   
--------------------------------
               /           /a\ \
             4 |      2*cot|-| |
/       2/a\\  |           \2/ |
|1 + cot |-|| *|1 + -----------|
\        \4//  |           2/a\|
               |    1 + cot |-||
               \            \2//

$$\frac{16 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \cot^{4}{\left(\frac{a}{4} \right)}}{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}}$$

1 - sin(a)

$$1 - \sin{\left(a \right)}$$

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

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

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

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

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

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

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

$$\frac{1}{\left(1 + \frac{1}{\csc{\left(a \right)}}\right) \sec^{2}{\left(a \right)}}$$

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

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

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

$$\frac{\cos{\left(2 a \right)} + 1}{2 \left(\sin{\left(a \right)} + 1\right)}$$

                 2                
   /        2/a\\     4/a\    8/a\
16*|-1 + cot |-|| *cot |-|*sin |-|
   \         \2//      \4/     \4/
----------------------------------
            1 + sin(a)

$$\frac{16 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{a}{4} \right)} \cot^{4}{\left(\frac{a}{4} \right)}}{\sin{\left(a \right)} + 1}$$

       /    pi\
1 - cos|a - --|
       \    2 /

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

         1     
1 - -----------
       /    pi\
    sec|a - --|
       \    2 /

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

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

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

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

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

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

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

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

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

      1   
1 - ------
    csc(a)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                    2           
      /        1   \     4/a\   
   16*|-1 + -------| *tan |-|   
      |        2/a\|      \4/   
      |     tan |-||            
      \         \2//            
--------------------------------
               /           /a\ \
             4 |      2*tan|-| |
/       2/a\\  |           \2/ |
|1 + tan |-|| *|1 + -----------|
\        \4//  |           2/a\|
               |    1 + tan |-||
               \            \2//

$$\frac{16 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \tan^{4}{\left(\frac{a}{4} \right)}}{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}}$$

16*(-1 + tan(a/2)^(-2))^2*tan(a/4)^4/((1 + tan(a/4)^2)^4*(1 + 2*tan(a/2)/(1 + tan(a/2)^2)))

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

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

Solución