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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x)+coscos(x)/(sin*sin(x))

¿Cómo vas a descomponer esta tan(x)+coscos(x)/(sin*sin(x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
          cos(cos(x)) 
tan(x) + -------------
         sin(x)*sin(x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡(x)sin⁡(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin{\left(x \right)} \sin{\left(x \right)}} 
tan(x) + cos(cos(x))/((sin(x)*sin(x)))
Simplificación general [src] 
cos(cos(x))         
----------- + tan(x)
     2              
  sin (x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
cos(cos(x))/sin(x)^2 + tan(x)
Potencias [src] 
    /   / I*x    -I*x\      /   I*x    -I*x\\                     
    |   |e      e    |      |  e      e    ||                     
    | I*|---- + -----|    I*|- ---- - -----||                     
    |   \ 2       2  /      \   2       2  /|                     
    |e                   e                  |                     
  4*|----------------- + -------------------|     /   I*x    -I*x\
    \        2                    2         /   I*\- e    + e    /
- ------------------------------------------- + ------------------
                               2                    I*x    -I*x   
               /   -I*x    I*x\                    e    + e       
               \- e     + e   /
i(−eix+e−ix)eix+e−ix−4(ei(−eix2−e−ix2)2+ei(eix2+e−ix2)2)(eix−e−ix)2\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} - \frac{4 \left(\frac{e^{i \left(- \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)}}{2} + \frac{e^{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}}{2}\right)}{\left(e^{i x} - e^{- i x}\right)^{2}} 
cos(cos(x))         
----------- + tan(x)
     2              
  sin (x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
cos(cos(x))/sin(x)^2 + tan(x)
Respuesta numérica [src] 
cos(cos(x))/sin(x)^2 + tan(x)
cos(cos(x))/sin(x)^2 + tan(x)
Denominador común [src] 
cos(cos(x))         
----------- + tan(x)
     2              
  sin (x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
cos(cos(x))/sin(x)^2 + tan(x)
Denominador racional [src] 
   2                        
sin (x)*tan(x) + cos(cos(x))
----------------------------
             2              
          sin (x)
sin⁡2(x)tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)} + \cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
(sin(x)^2*tan(x) + cos(cos(x)))/sin(x)^2
Unión de expresiones racionales [src] 
   2                        
sin (x)*tan(x) + cos(cos(x))
----------------------------
             2              
          sin (x)
sin⁡2(x)tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)} + \cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
(sin(x)^2*tan(x) + cos(cos(x)))/sin(x)^2
Abrimos la expresión [src] 
cos(cos(x))         
----------- + tan(x)
     2              
  sin (x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
cos(cos(x))/sin(x)^2 + tan(x)
Combinatoria [src] 
   2                        
sin (x)*tan(x) + cos(cos(x))
----------------------------
             2              
          sin (x)
sin⁡2(x)tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)} + \cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
(sin(x)^2*tan(x) + cos(cos(x)))/sin(x)^2
Compilar la expresión [src] 
cos(cos(x))         
----------- + tan(x)
     2              
  sin (x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
cos(cos(x))/sin(x)^2 + tan(x)
Parte trigonométrica [src] 
                   2   
cos(cos(x))   2*sin (x)
----------- + ---------
     2         sin(2*x)
  sin (x)
2sin⁡2(x)sin⁡(2x)+cos⁡(cos⁡(x))sin⁡2(x)\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
sin(x)   cos(cos(x))
------ + -----------
cos(x)        2     
           sin (x)
sin⁡(x)cos⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
               /        /         2/x\  \\         
             2 |        |  1 - tan |-|  ||         
/       2/x\\  |       2|          \2/  ||         
|1 + tan |-|| *|1 - tan |---------------||         
\        \2//  |        |  /       2/x\\||         
               |        |2*|1 + tan |-||||         
               \        \  \        \2////         
------------------------------------------ + tan(x)
    /        /         2/x\  \\                    
    |        |  1 - tan |-|  ||                    
    |       2|          \2/  ||    2/x\            
  4*|1 + tan |---------------||*tan |-|            
    |        |  /       2/x\\||     \2/            
    |        |2*|1 + tan |-||||                    
    \        \  \        \2////
(1−tan⁡2(1−tan⁡2(x2)2(tan⁡2(x2)+1)))(tan⁡2(x2)+1)24(tan⁡2(1−tan⁡2(x2)2(tan⁡2(x2)+1))+1)tan⁡2(x2)+tan⁡(x)\frac{\left(1 - \tan^{2}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 \left(\tan^{2}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} + 1\right) \tan^{2}{\left(\frac{x}{2} \right)}} + \tan{\left(x \right)} 
                        /         /          2/x\ \\
                      2 |         |  -1 + cot |-| ||
         /       2/x\\  |        2|           \2/ ||
         |1 + cot |-|| *|-1 + cot |---------------||
         \        \2//  |         |  /       2/x\\||
                        |         |2*|1 + cot |-||||
  1                     \         \  \        \2////
------ + -------------------------------------------
cot(x)        /        /          2/x\ \\           
              |        |  -1 + cot |-| ||           
              |       2|           \2/ ||    2/x\   
            4*|1 + cot |---------------||*cot |-|   
              |        |  /       2/x\\||     \2/   
              |        |2*|1 + cot |-||||           
              \        \  \        \2////
(cot⁡2(x2)+1)2(cot⁡2(cot⁡2(x2)−12(cot⁡2(x2)+1))−1)4(cot⁡2(cot⁡2(x2)−12(cot⁡2(x2)+1))+1)cot⁡2(x2)+1cot⁡(x)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} - 1\right)}{4 \left(\cot^{2}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} + 1\right) \cot^{2}{\left(\frac{x}{2} \right)}} + \frac{1}{\cot{\left(x \right)}} 
   /pi      /    pi\\            
sin|-- + sin|x + --||        2   
   \2       \    2 //   2*sin (x)
--------------------- + ---------
          2              sin(2*x)
       sin (x)
2sin⁡2(x)sin⁡(2x)+sin⁡(sin⁡(x+π2)+π2)sin⁡2(x)\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \frac{\sin{\left(\sin{\left(x + \frac{\pi}{2} \right)} + \frac{\pi}{2} \right)}}{\sin^{2}{\left(x \right)}} 
   2/pi    \              
sec |-- - x|              
    \2     /      sec(x)  
------------ + -----------
   /  1   \       /    pi\
sec|------|    sec|x - --|
   \sec(x)/       \    2 /
sec⁡(x)sec⁡(x−π2)+sec⁡2(−x+π2)sec⁡(1sec⁡(x))\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\sec^{2}{\left(- x + \frac{\pi}{2} \right)}}{\sec{\left(\frac{1}{\sec{\left(x \right)}} \right)}} 
   /    pi\               
cos|x - --|               
   \    2 /   cos(cos(x)) 
----------- + ------------
   cos(x)        2/    pi\
              cos |x - --|
                  \    2 /
cos⁡(cos⁡(x))cos⁡2(x−π2)+cos⁡(x−π2)cos⁡(x)\frac{\cos{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} 
   2/    pi\              
sec |x - --|              
    \    2 /      sec(x)  
------------ + -----------
   /  1   \       /    pi\
sec|------|    sec|x - --|
   \sec(x)/       \    2 /
sec⁡(x)sec⁡(x−π2)+sec⁡2(x−π2)sec⁡(1sec⁡(x))\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(\frac{1}{\sec{\left(x \right)}} \right)}} 
cos(cos(x))         
----------- + tan(x)
     2              
  sin (x)
tan⁡(x)+cos⁡(cos⁡(x))sin⁡2(x)\tan{\left(x \right)} + \frac{\cos{\left(\cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} 
   2                        
csc (x)*cos(cos(x)) + tan(x)
cos⁡(cos⁡(x))csc⁡2(x)+tan⁡(x)\cos{\left(\cos{\left(x \right)} \right)} \csc^{2}{\left(x \right)} + \tan{\left(x \right)} 
              2     
sec(x)     csc (x)  
------ + -----------
csc(x)      /  1   \
         sec|------|
            \sec(x)/
csc⁡2(x)sec⁡(1sec⁡(x))+sec⁡(x)csc⁡(x)\frac{\csc^{2}{\left(x \right)}}{\sec{\left(\frac{1}{\sec{\left(x \right)}} \right)}} + \frac{\sec{\left(x \right)}}{\csc{\left(x \right)}} 
   /pi    \                   
csc|-- - x|          2        
   \2     /       csc (x)     
----------- + ----------------
   csc(x)        /pi     1   \
              csc|-- - ------|
                 \2    sec(x)/
csc⁡2(x)csc⁡(π2−1sec⁡(x))+csc⁡(−x+π2)csc⁡(x)\frac{\csc^{2}{\left(x \right)}}{\csc{\left(\frac{\pi}{2} - \frac{1}{\sec{\left(x \right)}} \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} 
csc(pi/2 - x)/csc(x) + csc(x)^2/csc(pi/2 - 1/sec(x))
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