Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
¿cómo vas a descomponer esta expresión en fracciones?:
(x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
(z-a)/(5*z-2*a)-(z-4*a)/(z)
((z)-(7*z/z+3))*((z+3)/(z-4))
z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z)
Factorizar el polinomio:
z^2-8*p*z-z+4*p+16*p^2
z^2-6*z+10
z^2+5*z-6
z^2+6*z+1
Descomponer al cuadrado:
y^4-y^2+9
y^4+y^2-8
-y^4+y^2+9
y^4-y^2-5
Expresiones idénticas
(cos^2x)/(sinx-cosx)
( coseno de al cuadrado x) dividir por ( seno de x menos coseno de x)
(cos2x)/(sinx-cosx)
cos2x/sinx-cosx
(cos²x)/(sinx-cosx)
(cos en el grado 2x)/(sinx-cosx)
cos^2x/sinx-cosx
(cos^2x) dividir por (sinx-cosx)
Expresiones semejantes
(cos^2x)/(sinx+cosx)
Expresiones con funciones
Coseno cos
cos^2a/(1+sina)
cos(10*x)/(cos(5*x)-sin(5*x))
cos(x)/(2*sqrt(x))-sqrt(x)*sin(x)
cos(10*a)/(cos(5*a)-sin(5)*a)
cos(x-sin(x))/(4*x-pi)
sinx
sinx/(n*sin(2x-2arcsin(sinx/n)))
sinx/(1.5*sin(2x-2arcsin(sinx/1.5)))
sinx/(tan((pi/4)-(x/2))*(1+sinx))
sinx/(4-cos^2x)
sinx/(((1+tgx/2)/(1-tgx/2))*(1+sinx))

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

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

Solución

Ha introducido [src]

       2       
    cos (x)    
---------------
sin(x) - cos(x)

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

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

Combinatoria [src]

       2        
   -cos (x)     
----------------
-sin(x) + cos(x)

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

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

Denominador común [src]

                          2        
                       sin (x)     
-cos(x) - sin(x) - ----------------
                   -sin(x) + cos(x)

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

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

Potencias [src]

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

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

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

Parte trigonométrica [src]

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

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

                      2              
       /         4/x\\               
       |    4*sin |-||               
   ___ |          \2/|     4/pi   x\ 
-\/ 2 *|1 - ---------| *sin |-- + -| 
       |        2    |      \2    2/ 
       \     sin (x) /               
-------------------------------------
                /    3*pi\           
           2*sin|x + ----|           
                \     4  /

$$- \frac{\sqrt{2} \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{2} \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sin{\left(x + \frac{3 \pi}{4} \right)}}$$

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

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

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

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

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

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

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

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

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

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

   ___    2/    pi\ 
-\/ 2 *sin |x + --| 
           \    2 / 
--------------------
       /    3*pi\   
  2*sin|x + ----|   
       \     4  /

$$- \frac{\sqrt{2} \sin^{2}{\left(x + \frac{\pi}{2} \right)}}{2 \sin{\left(x + \frac{3 \pi}{4} \right)}}$$

                     2                    
   ___ /        2/x\\  /       2/x   pi\\ 
-\/ 2 *|-1 + cot |-|| *|1 + cot |- + --|| 
       \         \2//  \        \2   8 // 
------------------------------------------
                  2                       
     /       2/x\\  /        2/x   pi\\   
   2*|1 + cot |-|| *|-1 + cot |- + --||   
     \        \2//  \         \2   8 //

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

                    2               4                    
   ___ /       1   \  /        2/x\\  /       2/x   pi\\ 
-\/ 2 *|1 - -------| *|-1 + cot |-|| *|1 + cot |- + --|| 
       |       2/x\|  \         \4//  \        \2   8 // 
       |    cot |-||                                     
       \        \2//                                     
---------------------------------------------------------
                          4                              
             /       2/x\\  /        2/x   pi\\          
           2*|1 + cot |-|| *|-1 + cot |- + --||          
             \        \4//  \         \2   8 //

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                    2                    
   ___ /       2/x\\  /       2/x   pi\\ 
-\/ 2 *|1 - tan |-|| *|1 + tan |- + --|| 
       \        \2//  \        \2   8 // 
-----------------------------------------
                  2                      
     /       2/x\\  /       2/x   pi\\   
   2*|1 + tan |-|| *|1 - tan |- + --||   
     \        \2//  \        \2   8 //

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

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

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

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

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

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

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

   ___    2       /    pi\ 
-\/ 2 *cos (x)*sec|x + --| 
                  \    4 / 
---------------------------
             2

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

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

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

                     2                      
   ___ /        1   \     4/x\    /     pi\ 
-\/ 2 *|-1 + -------| *sin |-|*csc|-x + --| 
       |        2/x\|      \2/    \     4 / 
       |     tan |-||                       
       \         \2//                       
--------------------------------------------
                     2

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

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

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

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

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

                       2                           
     ___ /        1   \     4/x\ /       2/x   pi\\
-8*\/ 2 *|-1 + -------| *tan |-|*|1 + tan |- + --||
         |        2/x\|      \4/ \        \2   8 //
         |     tan |-||                            
         \         \2//                            
---------------------------------------------------
                      4                            
         /       2/x\\  /       2/x   pi\\         
         |1 + tan |-|| *|1 - tan |- + --||         
         \        \4//  \        \2   8 //

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

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

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

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

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

   ___    /     pi\ 
-\/ 2 *csc|-x + --| 
          \     4 / 
--------------------
        2/pi    \   
   2*csc |-- - x|   
         \2     /

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

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

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

                    2              4                    
   ___ /       2/x\\  /       2/x\\  /       2/x   pi\\ 
-\/ 2 *|1 - tan |-|| *|1 - tan |-|| *|1 + tan |- + --|| 
       \        \2//  \        \4//  \        \2   8 // 
--------------------------------------------------------
                         4                              
            /       2/x\\  /       2/x   pi\\           
          2*|1 + tan |-|| *|1 - tan |- + --||           
            \        \4//  \        \2   8 //

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

                       2         
       /         2    \          
   ___ |      sin (x) |     4/x\ 
-\/ 2 *|-1 + ---------| *sin |-| 
       |          4/x\|      \2/ 
       |     4*sin |-||          
       \           \2//          
---------------------------------
              /    3*pi\         
         2*sin|x + ----|         
              \     4  /

$$- \frac{\sqrt{2} \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}}{2 \sin{\left(x + \frac{3 \pi}{4} \right)}}$$

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

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

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

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

   ___    /    pi\ 
-\/ 2 *sec|x + --| 
          \    4 / 
-------------------
          2        
     2*sec (x)

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

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

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

                       2                           
     ___ /        2/x\\     4/x\ /       2/x   pi\\
-8*\/ 2 *|-1 + cot |-|| *cot |-|*|1 + cot |- + --||
         \         \2//      \4/ \        \2   8 //
---------------------------------------------------
                      4                            
         /       2/x\\  /        2/x   pi\\        
         |1 + cot |-|| *|-1 + cot |- + --||        
         \        \4//  \         \2   8 //

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

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

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

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

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

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

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

-sqrt(2)*(1 - tan(x/2)^2)^2*cos(x/2)^4*(1 + tan(x/2 + pi/8)^2)/(2*(1 - tan(x/2 + pi/8)^2))

Respuesta numérica [src]

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

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

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

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

Solución