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Simplificación de expresiones/ Descomposición en fracciones simples/ ctg(3п/2-а)/(1-tg^2a)

¿Cómo vas a descomponer esta ctg(3п/2-а)/(1-tg^2a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /3*pi    \
cot|---- - a|
   \ 2      /
-------------
        2    
 1 - tan (a)
cot⁡(−a+3π2)1−tan⁡2(a)\frac{\cot{\left(- a + \frac{3 \pi}{2} \right)}}{1 - \tan^{2}{\left(a \right)}} 
cot((3*pi)/2 - a)/(1 - tan(a)^2)
Descomposición de una fracción [src] 
-1/(2*(1 + tan(a))) - 1/(2*(-1 + tan(a)))
−12(tan⁡(a)+1)−12(tan⁡(a)−1)- \frac{1}{2 \left(\tan{\left(a \right)} + 1\right)} - \frac{1}{2 \left(\tan{\left(a \right)} - 1\right)} 
        1                 1       
- -------------- - ---------------
  2*(1 + tan(a))   2*(-1 + tan(a))
Simplificación general [src] 
tan(2*a)
--------
   2
tan⁡(2a)2\frac{\tan{\left(2 a \right)}}{2} 
tan(2*a)/2
Respuesta numérica [src] 
cot((3*pi)/2 - a)/(1.0 - tan(a)^2)
cot((3*pi)/2 - a)/(1.0 - tan(a)^2)
Potencias [src] 
        tan(a)       
---------------------
                    2
    /   I*a    -I*a\ 
    \- e    + e    / 
1 + -----------------
                   2 
     / I*a    -I*a\  
     \e    + e    /
tan⁡(a)(−eia+e−ia)2(eia+e−ia)2+1\frac{\tan{\left(a \right)}}{\frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} + 1} 
   tan(a)  
-----------
       2   
1 - tan (a)
tan⁡(a)1−tan⁡2(a)\frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}} 
tan(a)/(1 - tan(a)^2)
Unión de expresiones racionales [src] 
   /-2*a + 3*pi\
cot|-----------|
   \     2     /
----------------
         2      
  1 - tan (a)
cot⁡(−2a+3π2)1−tan⁡2(a)\frac{\cot{\left(\frac{- 2 a + 3 \pi}{2} \right)}}{1 - \tan^{2}{\left(a \right)}} 
cot((-2*a + 3*pi)/2)/(1 - tan(a)^2)
Combinatoria [src] 
         -tan(a)          
--------------------------
(1 + tan(a))*(-1 + tan(a))
−tan⁡(a)(tan⁡(a)−1)(tan⁡(a)+1)- \frac{\tan{\left(a \right)}}{\left(\tan{\left(a \right)} - 1\right) \left(\tan{\left(a \right)} + 1\right)} 
-tan(a)/((1 + tan(a))*(-1 + tan(a)))
Denominador común [src] 
  -tan(a)   
------------
        2   
-1 + tan (a)
−tan⁡(a)tan⁡2(a)−1- \frac{\tan{\left(a \right)}}{\tan^{2}{\left(a \right)} - 1} 
-tan(a)/(-1 + tan(a)^2)
Denominador racional [src] 
  -tan(a)   
------------
        2   
-1 + tan (a)
−tan⁡(a)tan⁡2(a)−1- \frac{\tan{\left(a \right)}}{\tan^{2}{\left(a \right)} - 1} 
-tan(a)/(-1 + tan(a)^2)
Abrimos la expresión [src] 
   tan(a)  
-----------
       2   
1 - tan (a)
tan⁡(a)1−tan⁡2(a)\frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}} 
tan(a)/(1 - tan(a)^2)
Parte trigonométrica [src] 
         1          
--------------------
/       1   \       
|1 - -------|*cot(a)
|       2   |       
\    cot (a)/
1(1−1cot⁡2(a))cot⁡(a)\frac{1}{\left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \cot{\left(a \right)}} 
   2     
sin (2*a)
---------
 sin(4*a)
sin⁡2(2a)sin⁡(4a)\frac{\sin^{2}{\left(2 a \right)}}{\sin{\left(4 a \right)}} 
    sec(2*a)   
---------------
     /      pi\
2*sec|2*a - --|
     \      2 /
sec⁡(2a)2sec⁡(2a−π2)\frac{\sec{\left(2 a \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}} 
   tan(a)  
-----------
       2   
1 - tan (a)
tan⁡(a)1−tan⁡2(a)\frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}} 
         1          
--------------------
/       2   \       
\1 - tan (a)/*cot(a)
1(1−tan⁡2(a))cot⁡(a)\frac{1}{\left(1 - \tan^{2}{\left(a \right)}\right) \cot{\left(a \right)}} 
   /      pi\
cos|2*a - --|
   \      2 /
-------------
  2*cos(2*a)
cos⁡(2a−π2)2cos⁡(2a)\frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a \right)}} 
   /pi      \
csc|-- - 2*a|
   \2       /
-------------
  2*csc(2*a)
csc⁡(−2a+π2)2csc⁡(2a)\frac{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}{2 \csc{\left(2 a \right)}} 
         sin(2*a)        
-------------------------
  /         4   \        
  |    4*sin (a)|    2   
2*|1 - ---------|*cos (a)
  |       2     |        
  \    sin (2*a)/
sin⁡(2a)2(−4sin⁡4(a)sin⁡2(2a)+1)cos⁡2(a)\frac{\sin{\left(2 a \right)}}{2 \left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \cos^{2}{\left(a \right)}} 
           sin(2*a)           
------------------------------
  /         4   \             
  |    4*sin (a)|    2/    pi\
2*|1 - ---------|*sin |a + --|
  |       2     |     \    2 /
  \    sin (2*a)/
sin⁡(2a)2(−4sin⁡4(a)sin⁡2(2a)+1)sin⁡2(a+π2)\frac{\sin{\left(2 a \right)}}{2 \left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin^{2}{\left(a + \frac{\pi}{2} \right)}} 
            sec(a)            
------------------------------
/         2      \            
|      sec (a)   |    /    pi\
|1 - ------------|*sec|a - --|
|       2/    pi\|    \    2 /
|    sec |a - --||            
\        \    2 //
sec⁡(a)(−sec⁡2(a)sec⁡2(a−π2)+1)sec⁡(a−π2)\frac{\sec{\left(a \right)}}{\left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(a - \frac{\pi}{2} \right)}} 
           -sin(a)            
------------------------------
/       2/    pi\\            
|    cos |a - --||            
|        \    2 /|            
|1 - ------------|*cos(pi - a)
|         2      |            
\      cos (a)   /
−sin⁡(a)(1−cos⁡2(a−π2)cos⁡2(a))cos⁡(π−a)- \frac{\sin{\left(a \right)}}{\left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos{\left(\pi - a \right)}} 
   tan(a)  
-----------
       1   
1 - -------
       2   
    cot (a)
tan⁡(a)1−1cot⁡2(a)\frac{\tan{\left(a \right)}}{1 - \frac{1}{\cot^{2}{\left(a \right)}}} 
tan(2*a)
--------
   2
tan⁡(2a)2\frac{\tan{\left(2 a \right)}}{2} 
    1     
----------
2*cot(2*a)
12cot⁡(2a)\frac{1}{2 \cot{\left(2 a \right)}} 
       sec(a)       
--------------------
/       2   \       
|    sec (a)|       
|1 - -------|*csc(a)
|       2   |       
\    csc (a)/
sec⁡(a)(1−sec⁡2(a)csc⁡2(a))csc⁡(a)\frac{\sec{\left(a \right)}}{\left(1 - \frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}} 
          /pi    \       
       csc|-- - a|       
          \2     /       
-------------------------
/       2/pi    \\       
|    csc |-- - a||       
|        \2     /|       
|1 - ------------|*csc(a)
|         2      |       
\      csc (a)   /
csc⁡(−a+π2)(1−csc⁡2(−a+π2)csc⁡2(a))csc⁡(a)\frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}} 
       /    pi\     
    cos|a - --|     
       \    2 /     
--------------------
/       2   \       
|    sin (a)|       
|1 - -------|*cos(a)
|       2   |       
\    cos (a)/
cos⁡(a−π2)(−sin⁡2(a)cos⁡2(a)+1)cos⁡(a)\frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\left(- \frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} + 1\right) \cos{\left(a \right)}} 
cos(a - pi/2)/((1 - sin(a)^2/cos(a)^2)*cos(a))
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