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Simplificación de expresiones/ Descomposición en fracciones simples/ cos^2x+1/(1+ctg^2(x))-1

¿Cómo vas a descomponer esta cos^2x+1/(1+ctg^2(x))-1 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2           1         
cos (x) + ----------- - 1
                 2       
          1 + cot (x)
(cos⁡2(x)+1cot⁡2(x)+1)−1\left(\cos^{2}{\left(x \right)} + \frac{1}{\cot^{2}{\left(x \right)} + 1}\right) - 1 
cos(x)^2 + 1/(1 + cot(x)^2) - 1
Simplificación general [src] 
0
00 
0
Respuesta numérica [src] 
-1.0 + 1/(1.0 + cot(x)^2) + cos(x)^2
-1.0 + 1/(1.0 + cot(x)^2) + cos(x)^2
Denominador común [src] 
          1           2   
-1 + ----------- + cos (x)
            2             
     1 + cot (x)
cos⁡2(x)−1+1cot⁡2(x)+1\cos^{2}{\left(x \right)} - 1 + \frac{1}{\cot^{2}{\left(x \right)} + 1} 
-1 + 1/(1 + cot(x)^2) + cos(x)^2
Denominador racional [src] 
     2         2    /       2   \
- cot (x) + cos (x)*\1 + cot (x)/
---------------------------------
                  2              
           1 + cot (x)
(cot⁡2(x)+1)cos⁡2(x)−cot⁡2(x)cot⁡2(x)+1\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} - \cot^{2}{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} 
(-cot(x)^2 + cos(x)^2*(1 + cot(x)^2))/(1 + cot(x)^2)
Unión de expresiones racionales [src] 
     2         2    /       2   \
- cot (x) + cos (x)*\1 + cot (x)/
---------------------------------
                  2              
           1 + cot (x)
(cot⁡2(x)+1)cos⁡2(x)−cot⁡2(x)cot⁡2(x)+1\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} - \cot^{2}{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} 
(-cot(x)^2 + cos(x)^2*(1 + cot(x)^2))/(1 + cot(x)^2)
Combinatoria [src] 
   2         2         2       2   
cos (x) - cot (x) + cos (x)*cot (x)
-----------------------------------
                   2               
            1 + cot (x)
cos⁡2(x)cot⁡2(x)+cos⁡2(x)−cot⁡2(x)cot⁡2(x)+1\frac{\cos^{2}{\left(x \right)} \cot^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - \cot^{2}{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} 
(cos(x)^2 - cot(x)^2 + cos(x)^2*cot(x)^2)/(1 + cot(x)^2)
Potencias [src] 
          1           2   
-1 + ----------- + cos (x)
            2             
     1 + cot (x)
cos⁡2(x)−1+1cot⁡2(x)+1\cos^{2}{\left(x \right)} - 1 + \frac{1}{\cot^{2}{\left(x \right)} + 1} 
                                 2
                   / I*x    -I*x\ 
          1        |e      e    | 
-1 + ----------- + |---- + -----| 
            2      \ 2       2  / 
     1 + cot (x)
(eix2+e−ix2)2−1+1cot⁡2(x)+1\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2} - 1 + \frac{1}{\cot^{2}{\left(x \right)} + 1} 
-1 + 1/(1 + cot(x)^2) + (exp(i*x)/2 + exp(-i*x)/2)^2
Parte trigonométrica [src] 
            1                1      
-1 + ---------------- + ------------
              2            2/pi    \
           csc (x)      csc |-- - x|
     1 + ------------       \2     /
            2/pi    \               
         csc |-- - x|               
             \2     /
−1+1csc⁡2(−x+π2)+1csc⁡2(x)csc⁡2(−x+π2)+1-1 + \frac{1}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} + 1} 
                                2
                   /       2/x\\ 
                   |1 - tan |-|| 
          1        \        \2// 
-1 + ----------- + --------------
            1                   2
     1 + -------   /       2/x\\ 
            2      |1 + tan |-|| 
         tan (x)   \        \2//
(1−tan⁡2(x2))2(tan⁡2(x2)+1)2−1+11+1tan⁡2(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - 1 + \frac{1}{1 + \frac{1}{\tan^{2}{\left(x \right)}}} 
            1              2   
-1 + ---------------- + cos (x)
              2                
           cos (x)             
     1 + ------------          
            2/    pi\          
         cos |x - --|          
             \    2 /
cos⁡2(x)−1+1cos⁡2(x)cos⁡2(x−π2)+1\cos^{2}{\left(x \right)} - 1 + \frac{1}{\frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} + 1} 
           1            2/    pi\
-1 + ------------- + sin |x + --|
            2            \    2 /
         sin (2*x)               
     1 + ---------               
              4                  
         4*sin (x)
sin⁡2(x+π2)−1+11+sin⁡2(2x)4sin⁡4(x)\sin^{2}{\left(x + \frac{\pi}{2} \right)} - 1 + \frac{1}{1 + \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}} 
            1              1   
-1 + ---------------- + -------
            2/    pi\      2   
         sec |x - --|   sec (x)
             \    2 /          
     1 + ------------          
              2                
           sec (x)
−1+1sec⁡2(x)+11+sec⁡2(x−π2)sec⁡2(x)-1 + \frac{1}{\sec^{2}{\left(x \right)}} + \frac{1}{1 + \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}} 
           1            2   
-1 + ------------- + cos (x)
            2               
         sin (2*x)          
     1 + ---------          
              4             
         4*sin (x)
cos⁡2(x)−1+11+sin⁡2(2x)4sin⁡4(x)\cos^{2}{\left(x \right)} - 1 + \frac{1}{1 + \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}} 
0
00 
          1           2   
-1 + ----------- + cos (x)
            2             
         cos (x)          
     1 + -------          
            2             
         sin (x)
cos⁡2(x)−1+11+cos⁡2(x)sin⁡2(x)\cos^{2}{\left(x \right)} - 1 + \frac{1}{1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}} 
                                 2
                   /        2/x\\ 
                   |-1 + cot |-|| 
          1        \         \2// 
-1 + ----------- + ---------------
            2                    2
     1 + cot (x)    /       2/x\\ 
                    |1 + cot |-|| 
                    \        \2//
(cot⁡2(x2)−1)2(cot⁡2(x2)+1)2−1+1cot⁡2(x)+1\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - 1 + \frac{1}{\cot^{2}{\left(x \right)} + 1} 
          1           1   
-1 + ----------- + -------
            2         2   
         csc (x)   sec (x)
     1 + -------          
            2             
         sec (x)
−1+1sec⁡2(x)+1csc⁡2(x)sec⁡2(x)+1-1 + \frac{1}{\sec^{2}{\left(x \right)}} + \frac{1}{\frac{\csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} + 1} 
-1 + 1/(1 + csc(x)^2/sec(x)^2) + sec(x)^(-2)
Compilar la expresión [src] 
          1           2   
-1 + ----------- + cos (x)
            2             
     1 + cot (x)
cos⁡2(x)−1+1cot⁡2(x)+1\cos^{2}{\left(x \right)} - 1 + \frac{1}{\cot^{2}{\left(x \right)} + 1} 
-1 + 1/(1 + cot(x)^2) + cos(x)^2
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