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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(360*pi/(360-x))

¿Cómo vas a descomponer esta tan(360*pi/(360-x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   / 360*pi\
tan|-------|
   \360 - x/
tan⁡(360π360−x)\tan{\left(\frac{360 \pi}{360 - x} \right)} 
tan((360*pi)/(360 - x))
Simplificación general [src] 
    / 360*pi \
-tan|--------|
    \-360 + x/
−tan⁡(360πx−360)- \tan{\left(\frac{360 \pi}{x - 360} \right)} 
-tan(360*pi/(-360 + x))
Respuesta numérica [src] 
tan((360*pi)/(360 - x))
tan((360*pi)/(360 - x))
Potencias [src] 
  /   360*pi*I    -360*pi*I\
  |   --------    ---------|
  |   360 - x      360 - x |
I*\- e         + e         /
----------------------------
    -360*pi*I    360*pi*I   
    ---------    --------   
     360 - x     360 - x    
   e          + e
i(−e360iπ360−x+e−360iπ360−x)e360iπ360−x+e−360iπ360−x\frac{i \left(- e^{\frac{360 i \pi}{360 - x}} + e^{- \frac{360 i \pi}{360 - x}}\right)}{e^{\frac{360 i \pi}{360 - x}} + e^{- \frac{360 i \pi}{360 - x}}} 
i*(-exp(360*pi*i/(360 - x)) + exp(-360*pi*i/(360 - x)))/(exp(-360*pi*i/(360 - x)) + exp(360*pi*i/(360 - x)))
Parte trigonométrica [src] 
     /  pi    720*pi\
2*sec|- -- + -------|
     \  2    360 - x/
---------------------
    2/  pi    360*pi\
 sec |- -- + -------|
     \  2    360 - x/
2sec⁡(−π2+720π360−x)sec⁡2(−π2+360π360−x)\frac{2 \sec{\left(- \frac{\pi}{2} + \frac{720 \pi}{360 - x} \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{360 \pi}{360 - x} \right)}} 
       / 360*pi\   
    sec|-------|   
       \360 - x/   
-------------------
   /  pi    360*pi\
sec|- -- + -------|
   \  2    360 - x/
sec⁡(360π360−x)sec⁡(−π2+360π360−x)\frac{\sec{\left(\frac{360 \pi}{360 - x} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{360 \pi}{360 - x} \right)}} 
     -1      
-------------
   / 360*pi \
cot|--------|
   \-360 + x/
−1cot⁡(360πx−360)- \frac{1}{\cot{\left(\frac{360 \pi}{x - 360} \right)}} 
   / 360*pi\
sec|-------|
   \360 - x/
------------
   / 360*pi\
csc|-------|
   \360 - x/
sec⁡(360π360−x)csc⁡(360π360−x)\frac{\sec{\left(\frac{360 \pi}{360 - x} \right)}}{\csc{\left(\frac{360 \pi}{360 - x} \right)}} 
     / 720*pi\
2*csc|-------|
     \360 - x/
--------------
   2/ 360*pi\ 
csc |-------| 
    \360 - x/
2csc⁡(720π360−x)csc⁡2(360π360−x)\frac{2 \csc{\left(\frac{720 \pi}{360 - x} \right)}}{\csc^{2}{\left(\frac{360 \pi}{360 - x} \right)}} 
     2/ 180*pi\ /       2/ 360*pi\\
4*cot |-------|*|1 + cot |-------||
      \360 - x/ \        \360 - x//
-----------------------------------
                    2              
 /       2/ 180*pi\\     / 360*pi\ 
 |1 + cot |-------|| *cot|-------| 
 \        \360 - x//     \360 - x/
4(cot⁡2(360π360−x)+1)cot⁡2(180π360−x)(cot⁡2(180π360−x)+1)2cot⁡(360π360−x)\frac{4 \left(\cot^{2}{\left(\frac{360 \pi}{360 - x} \right)} + 1\right) \cot^{2}{\left(\frac{180 \pi}{360 - x} \right)}}{\left(\cot^{2}{\left(\frac{180 \pi}{360 - x} \right)} + 1\right)^{2} \cot{\left(\frac{360 \pi}{360 - x} \right)}} 
      2/ 360*pi \
-2*sin |--------|
       \-360 + x/
-----------------
     / 720*pi \  
  sin|--------|  
     \-360 + x/
−2sin⁡2(360πx−360)sin⁡(720πx−360)- \frac{2 \sin^{2}{\left(\frac{360 \pi}{x - 360} \right)}}{\sin{\left(\frac{720 \pi}{x - 360} \right)}} 
    /  pi    360*pi \ 
-cos|- -- + --------| 
    \  2    -360 + x/ 
----------------------
       / 360*pi \     
    cos|--------|     
       \-360 + x/
−cos⁡(−π2+360πx−360)cos⁡(360πx−360)- \frac{\cos{\left(- \frac{\pi}{2} + \frac{360 \pi}{x - 360} \right)}}{\cos{\left(\frac{360 \pi}{x - 360} \right)}} 
     2/ 180*pi\ /       2/ 360*pi\\
4*tan |-------|*|1 + tan |-------||
      \360 - x/ \        \360 - x//
-----------------------------------
                    2              
 /       2/ 180*pi\\     / 360*pi\ 
 |1 + tan |-------|| *tan|-------| 
 \        \360 - x//     \360 - x/
4(tan⁡2(360π360−x)+1)tan⁡2(180π360−x)(tan⁡2(180π360−x)+1)2tan⁡(360π360−x)\frac{4 \left(\tan^{2}{\left(\frac{360 \pi}{360 - x} \right)} + 1\right) \tan^{2}{\left(\frac{180 \pi}{360 - x} \right)}}{\left(\tan^{2}{\left(\frac{180 \pi}{360 - x} \right)} + 1\right)^{2} \tan{\left(\frac{360 \pi}{360 - x} \right)}} 
   /pi    360*pi\
csc|-- - -------|
   \2    360 - x/
-----------------
      / 360*pi\  
   csc|-------|  
      \360 - x/
csc⁡(π2−360π360−x)csc⁡(360π360−x)\frac{\csc{\left(\frac{\pi}{2} - \frac{360 \pi}{360 - x} \right)}}{\csc{\left(\frac{360 \pi}{360 - x} \right)}} 
    /pi    360*pi \ 
-csc|-- - --------| 
    \2    -360 + x/ 
--------------------
      / 360*pi \    
   csc|--------|    
      \-360 + x/
−csc⁡(π2−360πx−360)csc⁡(360πx−360)- \frac{\csc{\left(\frac{\pi}{2} - \frac{360 \pi}{x - 360} \right)}}{\csc{\left(\frac{360 \pi}{x - 360} \right)}} 
   /  pi    360*pi\
cos|- -- + -------|
   \  2    360 - x/
-------------------
       / 360*pi\   
    cos|-------|   
       \360 - x/
cos⁡(−π2+360π360−x)cos⁡(360π360−x)\frac{\cos{\left(- \frac{\pi}{2} + \frac{360 \pi}{360 - x} \right)}}{\cos{\left(\frac{360 \pi}{360 - x} \right)}} 
   / 360*pi\
sin|-------|
   \360 - x/
------------
   / 360*pi\
cos|-------|
   \360 - x/
sin⁡(360π360−x)cos⁡(360π360−x)\frac{\sin{\left(\frac{360 \pi}{360 - x} \right)}}{\cos{\left(\frac{360 \pi}{360 - x} \right)}} 
      / 360*pi \    
  -sec|--------|    
      \-360 + x/    
--------------------
   /  pi    360*pi \
sec|- -- + --------|
   \  2    -360 + x/
−sec⁡(360πx−360)sec⁡(−π2+360πx−360)- \frac{\sec{\left(\frac{360 \pi}{x - 360} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{360 \pi}{x - 360} \right)}} 
    / 360*pi \
-tan|--------|
    \-360 + x/
−tan⁡(360πx−360)- \tan{\left(\frac{360 \pi}{x - 360} \right)} 
     1      
------------
   / 360*pi\
cot|-------|
   \360 - x/
1cot⁡(360π360−x)\frac{1}{\cot{\left(\frac{360 \pi}{360 - x} \right)}} 
     2/ 360*pi\
2*sin |-------|
      \360 - x/
---------------
     / 720*pi\ 
  sin|-------| 
     \360 - x/
2sin⁡2(360π360−x)sin⁡(720π360−x)\frac{2 \sin^{2}{\left(\frac{360 \pi}{360 - x} \right)}}{\sin{\left(\frac{720 \pi}{360 - x} \right)}} 
     2/  pi    360*pi\
2*cos |- -- + -------|
      \  2    360 - x/
----------------------
    /  pi    720*pi\  
 cos|- -- + -------|  
    \  2    360 - x/
2cos⁡2(−π2+360π360−x)cos⁡(−π2+720π360−x)\frac{2 \cos^{2}{\left(- \frac{\pi}{2} + \frac{360 \pi}{360 - x} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{720 \pi}{360 - x} \right)}} 
     4/ 180*pi \    2/ 180*pi \
4*cos |--------|*tan |--------|
      \-360 + x/     \-360 + x/
-------------------------------
     2/ 360*pi \    / 360*pi\  
  cos |--------|*tan|-------|  
      \-360 + x/    \360 - x/
4cos⁡4(180πx−360)tan⁡2(180πx−360)cos⁡2(360πx−360)tan⁡(360π360−x)\frac{4 \cos^{4}{\left(\frac{180 \pi}{x - 360} \right)} \tan^{2}{\left(\frac{180 \pi}{x - 360} \right)}}{\cos^{2}{\left(\frac{360 \pi}{x - 360} \right)} \tan{\left(\frac{360 \pi}{360 - x} \right)}} 
      2/ 180*pi\    4/ 180*pi \    / 360*pi \
-4*cot |-------|*sin |--------|*tan|--------|
       \360 - x/     \-360 + x/    \-360 + x/
---------------------------------------------
                   2/ 360*pi \               
                sin |--------|               
                    \-360 + x/
−4sin⁡4(180πx−360)tan⁡(360πx−360)cot⁡2(180π360−x)sin⁡2(360πx−360)- \frac{4 \sin^{4}{\left(\frac{180 \pi}{x - 360} \right)} \tan{\left(\frac{360 \pi}{x - 360} \right)} \cot^{2}{\left(\frac{180 \pi}{360 - x} \right)}}{\sin^{2}{\left(\frac{360 \pi}{x - 360} \right)}} 
-4*cot(180*pi/(360 - x))^2*sin(180*pi/(-360 + x))^4*tan(360*pi/(-360 + x))/sin(360*pi/(-360 + x))^2
Denominador racional [src] 
    / 360*pi \
-tan|--------|
    \-360 + x/
−tan⁡(360πx−360)- \tan{\left(\frac{360 \pi}{x - 360} \right)} 
-tan(360*pi/(-360 + x))
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