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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2nx)/(2n)-cos(2nx)/(4n^2)

¿Cómo vas a descomponer esta sin(2nx)/(2n)-cos(2nx)/(4n^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(2*n*x)   cos(2*n*x)
---------- - ----------
   2*n             2   
                4*n
−cos⁡(2nx)4n2+sin⁡(2nx)2n- \frac{\cos{\left(2 n x \right)}}{4 n^{2}} + \frac{\sin{\left(2 n x \right)}}{2 n} 
sin((2*n)*x)/((2*n)) - cos((2*n)*x)/(4*n^2)
Simplificación general [src] 
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
               2            
            4*n
2nsin⁡(2nx)−cos⁡(2nx)4n2\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}} 
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Respuesta numérica [src] 
0.5*sin((2*n)*x)/n - 0.25*cos((2*n)*x)/n^2
0.5*sin((2*n)*x)/n - 0.25*cos((2*n)*x)/n^2
Denominador racional [src] 
                     2           
-2*n*cos(2*n*x) + 4*n *sin(2*n*x)
---------------------------------
                  3              
               8*n
4n2sin⁡(2nx)−2ncos⁡(2nx)8n3\frac{4 n^{2} \sin{\left(2 n x \right)} - 2 n \cos{\left(2 n x \right)}}{8 n^{3}} 
(-2*n*cos(2*n*x) + 4*n^2*sin(2*n*x))/(8*n^3)
Combinatoria [src] 
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
               2            
            4*n
2nsin⁡(2nx)−cos⁡(2nx)4n2\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}} 
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Potencias [src] 
   -2*I*n*x    2*I*n*x                             
  e           e                                    
  --------- + --------     /   -2*I*n*x    2*I*n*x\
      2          2       I*\- e         + e       /
- -------------------- - --------------------------
             2                      4*n            
          4*n
−i(e2inx−e−2inx)4n−e2inx2+e−2inx24n2- \frac{i \left(e^{2 i n x} - e^{- 2 i n x}\right)}{4 n} - \frac{\frac{e^{2 i n x}}{2} + \frac{e^{- 2 i n x}}{2}}{4 n^{2}} 
sin(2*n*x)   cos(2*n*x)
---------- - ----------
   2*n             2   
                4*n
sin⁡(2nx)2n−cos⁡(2nx)4n2\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}} 
sin(2*n*x)/(2*n) - cos(2*n*x)/(4*n^2)
Denominador común [src] 
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
               2            
            4*n
2nsin⁡(2nx)−cos⁡(2nx)4n2\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}} 
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Unión de expresiones racionales [src] 
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
               2            
            4*n
2nsin⁡(2nx)−cos⁡(2nx)4n2\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}} 
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Abrimos la expresión [src] 
sin(2*n*x)   cos(2*n*x)
---------- - ----------
   2*n             2   
                4*n
sin⁡(2nx)2n−cos⁡(2nx)4n2\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}} 
sin((2*n)*x)/(2*n) - cos((2*n)*x)/(4*n^2)
Compilar la expresión [src] 
sin(2*n*x)   cos(2*n*x)
---------- - ----------
   2*n             2   
                4*n
sin⁡(2nx)2n−cos⁡(2nx)4n2\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}} 
sin((2*n)*x)/(2*n) - cos((2*n)*x)/(4*n^2)
Parte trigonométrica [src] 
      1                   1          
-------------- - --------------------
2*n*csc(2*n*x)      2    /pi        \
                 4*n *csc|-- - 2*n*x|
                         \2         /
12ncsc⁡(2nx)−14n2csc⁡(−2nx+π2)\frac{1}{2 n \csc{\left(2 n x \right)}} - \frac{1}{4 n^{2} \csc{\left(- 2 n x + \frac{\pi}{2} \right)}} 
     /  pi        \   cos(2*n*x)
2*cos|- -- + 2*n*x| - ----------
     \  2         /       n     
--------------------------------
              4*n
2cos⁡(2nx−π2)−cos⁡(2nx)n4n\frac{2 \cos{\left(2 n x - \frac{\pi}{2} \right)} - \frac{\cos{\left(2 n x \right)}}{n}}{4 n} 
        2                1      
----------------- - ------------
   /  pi        \   n*sec(2*n*x)
sec|- -- + 2*n*x|               
   \  2         /               
--------------------------------
              4*n
2sec⁡(2nx−π2)−1nsec⁡(2nx)4n\frac{\frac{2}{\sec{\left(2 n x - \frac{\pi}{2} \right)}} - \frac{1}{n \sec{\left(2 n x \right)}}}{4 n} 
                          2      
  4*cot(n*x)      -1 + cot (n*x) 
------------- - -----------------
       2          /       2     \
1 + cot (n*x)   n*\1 + cot (n*x)/
---------------------------------
               4*n
4cot⁡(nx)cot⁡2(nx)+1−cot⁡2(nx)−1n(cot⁡2(nx)+1)4n\frac{\frac{4 \cot{\left(n x \right)}}{\cot^{2}{\left(n x \right)} + 1} - \frac{\cot^{2}{\left(n x \right)} - 1}{n \left(\cot^{2}{\left(n x \right)} + 1\right)}}{4 n} 
          1                    1       
--------------------- - ---------------
       /  pi        \      2           
2*n*sec|- -- + 2*n*x|   4*n *sec(2*n*x)
       \  2         /
12nsec⁡(2nx−π2)−14n2sec⁡(2nx)\frac{1}{2 n \sec{\left(2 n x - \frac{\pi}{2} \right)}} - \frac{1}{4 n^{2} \sec{\left(2 n x \right)}} 
                  /pi        \
               sin|-- + 2*n*x|
                  \2         /
2*sin(2*n*x) - ---------------
                      n       
------------------------------
             4*n
2sin⁡(2nx)−sin⁡(2nx+π2)n4n\frac{2 \sin{\left(2 n x \right)} - \frac{\sin{\left(2 n x + \frac{\pi}{2} \right)}}{n}}{4 n} 
                /pi        \
             sin|-- + 2*n*x|
sin(2*n*x)      \2         /
---------- - ---------------
   2*n                2     
                   4*n
sin⁡(2nx)2n−sin⁡(2nx+π2)4n2\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\sin{\left(2 n x + \frac{\pi}{2} \right)}}{4 n^{2}} 
      1                 1       
-------------- - ---------------
2*n*csc(2*n*x)      2           
                 4*n *sec(2*n*x)
12ncsc⁡(2nx)−14n2sec⁡(2nx)\frac{1}{2 n \csc{\left(2 n x \right)}} - \frac{1}{4 n^{2} \sec{\left(2 n x \right)}} 
                         2       
  4*tan(n*x)      1 - tan (n*x)  
------------- - -----------------
       2          /       2     \
1 + tan (n*x)   n*\1 + tan (n*x)/
---------------------------------
               4*n
4tan⁡(nx)tan⁡2(nx)+1−1−tan⁡2(nx)n(tan⁡2(nx)+1)4n\frac{\frac{4 \tan{\left(n x \right)}}{\tan^{2}{\left(n x \right)} + 1} - \frac{1 - \tan^{2}{\left(n x \right)}}{n \left(\tan^{2}{\left(n x \right)} + 1\right)}}{4 n} 
sin(2*n*x)   cos(2*n*x)
---------- - ----------
   2*n             2   
                4*n
sin⁡(2nx)2n−cos⁡(2nx)4n2\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}} 
               cos(2*n*x)
2*sin(2*n*x) - ----------
                   n     
-------------------------
           4*n
2sin⁡(2nx)−cos⁡(2nx)n4n\frac{2 \sin{\left(2 n x \right)} - \frac{\cos{\left(2 n x \right)}}{n}}{4 n} 
                              2         
     tan(n*x)          1 - tan (n*x)    
----------------- - --------------------
  /       2     \      2 /       2     \
n*\1 + tan (n*x)/   4*n *\1 + tan (n*x)/
tan⁡(nx)n(tan⁡2(nx)+1)−1−tan⁡2(nx)4n2(tan⁡2(nx)+1)\frac{\tan{\left(n x \right)}}{n \left(\tan^{2}{\left(n x \right)} + 1\right)} - \frac{1 - \tan^{2}{\left(n x \right)}}{4 n^{2} \left(\tan^{2}{\left(n x \right)} + 1\right)} 
   /  pi        \             
cos|- -- + 2*n*x|             
   \  2         /   cos(2*n*x)
----------------- - ----------
       2*n                2   
                       4*n
cos⁡(2nx−π2)2n−cos⁡(2nx)4n2\frac{\cos{\left(2 n x - \frac{\pi}{2} \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}} 
    2                1        
---------- - -----------------
csc(2*n*x)        /pi        \
             n*csc|-- - 2*n*x|
                  \2         /
------------------------------
             4*n
2csc⁡(2nx)−1ncsc⁡(−2nx+π2)4n\frac{\frac{2}{\csc{\left(2 n x \right)}} - \frac{1}{n \csc{\left(- 2 n x + \frac{\pi}{2} \right)}}}{4 n} 
                               2        
     cot(n*x)          -1 + cot (n*x)   
----------------- - --------------------
  /       2     \      2 /       2     \
n*\1 + cot (n*x)/   4*n *\1 + cot (n*x)/
cot⁡(nx)n(cot⁡2(nx)+1)−cot⁡2(nx)−14n2(cot⁡2(nx)+1)\frac{\cot{\left(n x \right)}}{n \left(\cot^{2}{\left(n x \right)} + 1\right)} - \frac{\cot^{2}{\left(n x \right)} - 1}{4 n^{2} \left(\cot^{2}{\left(n x \right)} + 1\right)} 
cot(n*x)/(n*(1 + cot(n*x)^2)) - (-1 + cot(n*x)^2)/(4*n^2*(1 + cot(n*x)^2))
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