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Simplificación de expresiones/ Descomposición en fracciones simples/ sin^2(B)/(1-cos^2(B))+tg^2(B)

¿Cómo vas a descomponer esta sin^2(B)/(1-cos^2(B))+tg^2(B) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     2               
  sin (b)        2   
----------- + tan (b)
       2             
1 - cos (b)
tan⁡2(b)+sin⁡2(b)1−cos⁡2(b)\tan^{2}{\left(b \right)} + \frac{\sin^{2}{\left(b \right)}}{1 - \cos^{2}{\left(b \right)}} 
sin(b)^2/(1 - cos(b)^2) + tan(b)^2
Simplificación general [src] 
   1   
-------
   2   
cos (b)
1cos⁡2(b)\frac{1}{\cos^{2}{\left(b \right)}} 
cos(b)^(-2)
Respuesta numérica [src] 
tan(b)^2 + sin(b)^2/(1.0 - cos(b)^2)
tan(b)^2 + sin(b)^2/(1.0 - cos(b)^2)
Potencias [src] 
                  2                      2   
  /   I*b    -I*b\       /   -I*b    I*b\    
  \- e    + e    /       \- e     + e   /    
- ----------------- - -----------------------
                 2      /                  2\
   / I*b    -I*b\       |    / I*b    -I*b\ |
   \e    + e    /       |    |e      e    | |
                      4*|1 - |---- + -----| |
                        \    \ 2       2  / /
−(−eib+e−ib)2(eib+e−ib)2−(eib−e−ib)24(1−(eib2+e−ib2)2)- \frac{\left(- e^{i b} + e^{- i b}\right)^{2}}{\left(e^{i b} + e^{- i b}\right)^{2}} - \frac{\left(e^{i b} - e^{- i b}\right)^{2}}{4 \left(1 - \left(\frac{e^{i b}}{2} + \frac{e^{- i b}}{2}\right)^{2}\right)} 
-(-exp(i*b) + exp(-i*b))^2/(exp(i*b) + exp(-i*b))^2 - (-exp(-i*b) + exp(i*b))^2/(4*(1 - (exp(i*b)/2 + exp(-i*b)/2)^2))
Denominador racional [src] 
   2         2    /       2   \
sin (b) + tan (b)*\1 - cos (b)/
-------------------------------
                 2             
          1 - cos (b)
(1−cos⁡2(b))tan⁡2(b)+sin⁡2(b)1−cos⁡2(b)\frac{\left(1 - \cos^{2}{\left(b \right)}\right) \tan^{2}{\left(b \right)} + \sin^{2}{\left(b \right)}}{1 - \cos^{2}{\left(b \right)}} 
(sin(b)^2 + tan(b)^2*(1 - cos(b)^2))/(1 - cos(b)^2)
Denominador común [src] 
               2      
   2        sin (b)   
tan (b) - ------------
                  2   
          -1 + cos (b)
tan⁡2(b)−sin⁡2(b)cos⁡2(b)−1\tan^{2}{\left(b \right)} - \frac{\sin^{2}{\left(b \right)}}{\cos^{2}{\left(b \right)} - 1} 
tan(b)^2 - sin(b)^2/(-1 + cos(b)^2)
Unión de expresiones racionales [src] 
   2         2    /       2   \
sin (b) + tan (b)*\1 - cos (b)/
-------------------------------
                 2             
          1 - cos (b)
(1−cos⁡2(b))tan⁡2(b)+sin⁡2(b)1−cos⁡2(b)\frac{\left(1 - \cos^{2}{\left(b \right)}\right) \tan^{2}{\left(b \right)} + \sin^{2}{\left(b \right)}}{1 - \cos^{2}{\left(b \right)}} 
(sin(b)^2 + tan(b)^2*(1 - cos(b)^2))/(1 - cos(b)^2)
Parte trigonométrica [src] 
       2                4   
    sin (b)        4*sin (b)
---------------- + ---------
       2/    pi\      2     
1 - sin |b + --|   sin (2*b)
        \    2 /
4sin⁡4(b)sin⁡2(2b)+sin⁡2(b)1−sin⁡2(b+π2)\frac{4 \sin^{4}{\left(b \right)}}{\sin^{2}{\left(2 b \right)}} + \frac{\sin^{2}{\left(b \right)}}{1 - \sin^{2}{\left(b + \frac{\pi}{2} \right)}} 
     1      
------------
   2/    pi\
sin |b + --|
    \    2 /
1sin⁡2(b+π2)\frac{1}{\sin^{2}{\left(b + \frac{\pi}{2} \right)}} 
                                2/pi    \
                             csc |-- - b|
            1                    \2     /
-------------------------- + ------------
/         1      \    2           2      
|1 - ------------|*csc (b)     csc (b)   
|       2/pi    \|                       
|    csc |-- - b||                       
\        \2     //
csc⁡2(−b+π2)csc⁡2(b)+1(1−1csc⁡2(−b+π2))csc⁡2(b)\frac{\csc^{2}{\left(- b + \frac{\pi}{2} \right)}}{\csc^{2}{\left(b \right)}} + \frac{1}{\left(1 - \frac{1}{\csc^{2}{\left(- b + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(b \right)}} 
              2
 /       2/b\\ 
 |1 + cot |-|| 
 \        \2// 
---------------
              2
/        2/b\\ 
|-1 + cot |-|| 
\         \2//
(cot⁡2(b2)+1)2(cot⁡2(b2)−1)2\frac{\left(\cot^{2}{\left(\frac{b}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{b}{2} \right)} - 1\right)^{2}} 
                                  2      
            1                  sec (b)   
-------------------------- + ------------
/       1   \    2/    pi\      2/    pi\
|1 - -------|*sec |b - --|   sec |b - --|
|       2   |     \    2 /       \    2 /
\    sec (b)/
sec⁡2(b)sec⁡2(b−π2)+1(1−1sec⁡2(b))sec⁡2(b−π2)\frac{\sec^{2}{\left(b \right)}}{\sec^{2}{\left(b - \frac{\pi}{2} \right)}} + \frac{1}{\left(1 - \frac{1}{\sec^{2}{\left(b \right)}}\right) \sec^{2}{\left(b - \frac{\pi}{2} \right)}} 
     2      
------------
1 + cos(2*b)
2cos⁡(2b)+1\frac{2}{\cos{\left(2 b \right)} + 1} 
   2   
sec (b)
sec⁡2(b)\sec^{2}{\left(b \right)} 
   2/pi    \
csc |-- - b|
    \2     /
csc⁡2(−b+π2)\csc^{2}{\left(- b + \frac{\pi}{2} \right)} 
     2           2   
  sin (b)     sin (b)
----------- + -------
       2         2   
1 - cos (b)   cos (b)
sin⁡2(b)cos⁡2(b)+sin⁡2(b)1−cos⁡2(b)\frac{\sin^{2}{\left(b \right)}}{\cos^{2}{\left(b \right)}} + \frac{\sin^{2}{\left(b \right)}}{1 - \cos^{2}{\left(b \right)}} 
                            2/b\              
                       4*cot |-|              
   1                         \2/              
------- + ------------------------------------
   2                     /                  2\
cot (b)                  |    /        2/b\\ |
                       2 |    |-1 + cot |-|| |
          /       2/b\\  |    \         \2// |
          |1 + cot |-|| *|1 - ---------------|
          \        \2//  |                  2|
                         |     /       2/b\\ |
                         |     |1 + cot |-|| |
                         \     \        \2// /
1cot⁡2(b)+4cot⁡2(b2)(−(cot⁡2(b2)−1)2(cot⁡2(b2)+1)2+1)(cot⁡2(b2)+1)2\frac{1}{\cot^{2}{\left(b \right)}} + \frac{4 \cot^{2}{\left(\frac{b}{2} \right)}}{\left(- \frac{\left(\cot^{2}{\left(\frac{b}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{b}{2} \right)} + 1\right)^{2}} + 1\right) \left(\cot^{2}{\left(\frac{b}{2} \right)} + 1\right)^{2}} 
     2             4   
  sin (b)     4*sin (b)
----------- + ---------
       2         2     
1 - cos (b)   sin (2*b)
4sin⁡4(b)sin⁡2(2b)+sin⁡2(b)1−cos⁡2(b)\frac{4 \sin^{4}{\left(b \right)}}{\sin^{2}{\left(2 b \right)}} + \frac{\sin^{2}{\left(b \right)}}{1 - \cos^{2}{\left(b \right)}} 
   1   
-------
   2   
cos (b)
1cos⁡2(b)\frac{1}{\cos^{2}{\left(b \right)}} 
             2
/       2/b\\ 
|1 + tan |-|| 
\        \2// 
--------------
             2
/       2/b\\ 
|1 - tan |-|| 
\        \2//
(tan⁡2(b2)+1)2(1−tan⁡2(b2))2\frac{\left(\tan^{2}{\left(\frac{b}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{b}{2} \right)}\right)^{2}} 
                           2   
          1             sec (b)
--------------------- + -------
/       1   \    2         2   
|1 - -------|*csc (b)   csc (b)
|       2   |                  
\    sec (b)/
sec⁡2(b)csc⁡2(b)+1(1−1sec⁡2(b))csc⁡2(b)\frac{\sec^{2}{\left(b \right)}}{\csc^{2}{\left(b \right)}} + \frac{1}{\left(1 - \frac{1}{\sec^{2}{\left(b \right)}}\right) \csc^{2}{\left(b \right)}} 
   2/    pi\      2/    pi\
cos |b - --|   cos |b - --|
    \    2 /       \    2 /
------------ + ------------
       2            2      
1 - cos (b)      cos (b)
cos⁡2(b−π2)cos⁡2(b)+cos⁡2(b−π2)1−cos⁡2(b)\frac{\cos^{2}{\left(b - \frac{\pi}{2} \right)}}{\cos^{2}{\left(b \right)}} + \frac{\cos^{2}{\left(b - \frac{\pi}{2} \right)}}{1 - \cos^{2}{\left(b \right)}} 
                            2/b\             
                       4*tan |-|             
   2                         \2/             
tan (b) + -----------------------------------
                         /                 2\
                         |    /       2/b\\ |
                       2 |    |1 - tan |-|| |
          /       2/b\\  |    \        \2// |
          |1 + tan |-|| *|1 - --------------|
          \        \2//  |                 2|
                         |    /       2/b\\ |
                         |    |1 + tan |-|| |
                         \    \        \2// /
tan⁡2(b)+4tan⁡2(b2)(−(1−tan⁡2(b2))2(tan⁡2(b2)+1)2+1)(tan⁡2(b2)+1)2\tan^{2}{\left(b \right)} + \frac{4 \tan^{2}{\left(\frac{b}{2} \right)}}{\left(- \frac{\left(1 - \tan^{2}{\left(\frac{b}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{b}{2} \right)} + 1\right)^{2}} + 1\right) \left(\tan^{2}{\left(\frac{b}{2} \right)} + 1\right)^{2}} 
tan(b)^2 + 4*tan(b/2)^2/((1 + tan(b/2)^2)^2*(1 - (1 - tan(b/2)^2)^2/(1 + tan(b/2)^2)^2))
Combinatoria [src] 
     2         2         2       2   
- sin (b) - tan (b) + cos (b)*tan (b)
-------------------------------------
      (1 + cos(b))*(-1 + cos(b))
−sin⁡2(b)+cos⁡2(b)tan⁡2(b)−tan⁡2(b)(cos⁡(b)−1)(cos⁡(b)+1)\frac{- \sin^{2}{\left(b \right)} + \cos^{2}{\left(b \right)} \tan^{2}{\left(b \right)} - \tan^{2}{\left(b \right)}}{\left(\cos{\left(b \right)} - 1\right) \left(\cos{\left(b \right)} + 1\right)} 
(-sin(b)^2 - tan(b)^2 + cos(b)^2*tan(b)^2)/((1 + cos(b))*(-1 + cos(b)))
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