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Simplificación de expresiones/ Descomposición en fracciones simples/ tgA*ctgA-cos^2A/(2sinA)

¿Cómo vas a descomponer esta tgA*ctgA-cos^2A/(2sinA) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                   2    
                cos (a) 
tan(a)*cot(a) - --------
                2*sin(a)
tan⁡(a)cot⁡(a)−cos⁡2(a)2sin⁡(a)\tan{\left(a \right)} \cot{\left(a \right)} - \frac{\cos^{2}{\left(a \right)}}{2 \sin{\left(a \right)}} 
tan(a)*cot(a) - cos(a)^2/(2*sin(a))
Simplificación general [src] 
    sin(a)      1    
1 + ------ - --------
      2      2*sin(a)
sin⁡(a)2+1−12sin⁡(a)\frac{\sin{\left(a \right)}}{2} + 1 - \frac{1}{2 \sin{\left(a \right)}} 
1 + sin(a)/2 - 1/(2*sin(a))
Unión de expresiones racionales [src] 
     2                            
- cos (a) + 2*cot(a)*sin(a)*tan(a)
----------------------------------
             2*sin(a)
2sin⁡(a)tan⁡(a)cot⁡(a)−cos⁡2(a)2sin⁡(a)\frac{2 \sin{\left(a \right)} \tan{\left(a \right)} \cot{\left(a \right)} - \cos^{2}{\left(a \right)}}{2 \sin{\left(a \right)}} 
(-cos(a)^2 + 2*cot(a)*sin(a)*tan(a))/(2*sin(a))
Respuesta numérica [src] 
cot(a)*tan(a) - 0.5*cos(a)^2/sin(a)
cot(a)*tan(a) - 0.5*cos(a)^2/sin(a)
Denominador racional [src] 
     2                            
- cos (a) + 2*cot(a)*sin(a)*tan(a)
----------------------------------
             2*sin(a)
2sin⁡(a)tan⁡(a)cot⁡(a)−cos⁡2(a)2sin⁡(a)\frac{2 \sin{\left(a \right)} \tan{\left(a \right)} \cot{\left(a \right)} - \cos^{2}{\left(a \right)}}{2 \sin{\left(a \right)}} 
(-cos(a)^2 + 2*cot(a)*sin(a)*tan(a))/(2*sin(a))
Combinatoria [src] 
 /   2                            \ 
-\cos (a) - 2*cot(a)*sin(a)*tan(a)/ 
------------------------------------
              2*sin(a)
−−2sin⁡(a)tan⁡(a)cot⁡(a)+cos⁡2(a)2sin⁡(a)- \frac{- 2 \sin{\left(a \right)} \tan{\left(a \right)} \cot{\left(a \right)} + \cos^{2}{\left(a \right)}}{2 \sin{\left(a \right)}} 
-(cos(a)^2 - 2*cot(a)*sin(a)*tan(a))/(2*sin(a))
Potencias [src] 
                  2                            
    / I*a    -I*a\                             
    |e      e    |                             
  I*|---- + -----|      /   I*a    -I*a\       
    \ 2       2  /    I*\- e    + e    /*cot(a)
- ----------------- + -------------------------
       -I*a    I*a            I*a    -I*a      
    - e     + e              e    + e
i(−eia+e−ia)cot⁡(a)eia+e−ia−i(eia2+e−ia2)2eia−e−ia\frac{i \left(- e^{i a} + e^{- i a}\right) \cot{\left(a \right)}}{e^{i a} + e^{- i a}} - \frac{i \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{2}}{e^{i a} - e^{- i a}} 
-i*(exp(i*a)/2 + exp(-i*a)/2)^2/(-exp(-i*a) + exp(i*a)) + i*(-exp(i*a) + exp(-i*a))*cot(a)/(exp(i*a) + exp(-i*a))
Parte trigonométrica [src] 
                       /    pi\
                    sec|a - --|
          1            \    2 /
1 + ------------- - -----------
         /    pi\        2     
    2*sec|a - --|              
         \    2 /
−sec⁡(a−π2)2+1+12sec⁡(a−π2)- \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{2} + 1 + \frac{1}{2 \sec{\left(a - \frac{\pi}{2} \right)}} 
       /    pi\
    sec|a - --|
       \    2 /
1 - -----------
          2    
     2*sec (a)
1−sec⁡(a−π2)2sec⁡2(a)1 - \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{2 \sec^{2}{\left(a \right)}} 
                     2    
        /       2/a\\     
        |1 - tan |-||     
        \        \2//     
1 - ----------------------
      /       2/a\\    /a\
    4*|1 + tan |-||*tan|-|
      \        \2//    \2/
−(1−tan⁡2(a2))24(tan⁡2(a2)+1)tan⁡(a2)+1- \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{2}}{4 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}} + 1 
       /    pi\                
    cos|a - --|                
       \    2 /         1      
1 + ----------- - -------------
         2             /    pi\
                  2*cos|a - --|
                       \    2 /
cos⁡(a−π2)2+1−12cos⁡(a−π2)\frac{\cos{\left(a - \frac{\pi}{2} \right)}}{2} + 1 - \frac{1}{2 \cos{\left(a - \frac{\pi}{2} \right)}} 
    sin(a)      1    
1 + ------ - --------
      2      2*sin(a)
sin⁡(a)2+1−12sin⁡(a)\frac{\sin{\left(a \right)}}{2} + 1 - \frac{1}{2 \sin{\left(a \right)}} 
       /pi    \
    sec|-- - a|
       \2     /
1 - -----------
          2    
     2*sec (a)
1−sec⁡(−a+π2)2sec⁡2(a)1 - \frac{\sec{\left(- a + \frac{\pi}{2} \right)}}{2 \sec^{2}{\left(a \right)}} 
       2    
    cos (a) 
1 - --------
    2*sin(a)
1−cos⁡2(a)2sin⁡(a)1 - \frac{\cos^{2}{\left(a \right)}}{2 \sin{\left(a \right)}} 
          2      
       cos (a)   
1 - -------------
         /    pi\
    2*cos|a - --|
         \    2 /
−cos⁡2(a)2cos⁡(a−π2)+1- \frac{\cos^{2}{\left(a \right)}}{2 \cos{\left(a - \frac{\pi}{2} \right)}} + 1 
      csc(a) 
1 - ---------
         2   
    2*sec (a)
−csc⁡(a)2sec⁡2(a)+1- \frac{\csc{\left(a \right)}}{2 \sec^{2}{\left(a \right)}} + 1 
          /a\            2/a\
       tan|-|     1 + tan |-|
          \2/             \2/
1 + ----------- - -----------
           2/a\          /a\ 
    1 + tan |-|     4*tan|-| 
            \2/          \2/
−tan⁡2(a2)+14tan⁡(a2)+1+tan⁡(a2)tan⁡2(a2)+1- \frac{\tan^{2}{\left(\frac{a}{2} \right)} + 1}{4 \tan{\left(\frac{a}{2} \right)}} + 1 + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} 
    sin(a)   csc(a)
1 + ------ - ------
      2        2
sin⁡(a)2−csc⁡(a)2+1\frac{\sin{\left(a \right)}}{2} - \frac{\csc{\left(a \right)}}{2} + 1 
       1       csc(a)
1 + -------- - ------
    2*csc(a)     2
−csc⁡(a)2+1+12csc⁡(a)- \frac{\csc{\left(a \right)}}{2} + 1 + \frac{1}{2 \csc{\left(a \right)}} 
        csc(a)    
1 - --------------
         2/pi    \
    2*csc |-- - a|
          \2     /
−csc⁡(a)2csc⁡2(−a+π2)+1- \frac{\csc{\left(a \right)}}{2 \csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1 
          /a\            2/a\
       cot|-|     1 + cot |-|
          \2/             \2/
1 + ----------- - -----------
           2/a\          /a\ 
    1 + cot |-|     4*cot|-| 
            \2/          \2/
−cot⁡2(a2)+14cot⁡(a2)+1+cot⁡(a2)cot⁡2(a2)+1- \frac{\cot^{2}{\left(\frac{a}{2} \right)} + 1}{4 \cot{\left(\frac{a}{2} \right)}} + 1 + \frac{\cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} 
       2/    pi\
    sin |a + --|
        \    2 /
1 - ------------
      2*sin(a)
1−sin⁡2(a+π2)2sin⁡(a)1 - \frac{\sin^{2}{\left(a + \frac{\pi}{2} \right)}}{2 \sin{\left(a \right)}} 
                     2    
       /        2/a\\     
       |-1 + cot |-||     
       \         \2//     
1 - ----------------------
      /       2/a\\    /a\
    4*|1 + cot |-||*cot|-|
      \        \2//    \2/
−(cot⁡2(a2)−1)24(cot⁡2(a2)+1)cot⁡(a2)+1- \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{4 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}} + 1 
       2          
    cos (a)*csc(a)
1 - --------------
          2
−cos⁡2(a)csc⁡(a)2+1- \frac{\cos^{2}{\left(a \right)} \csc{\left(a \right)}}{2} + 1 
1 - cos(a)^2*csc(a)/2
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