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

Expresión a simplificar:

Solución

Ha introducido [src]
   1   
-------
   2   
cos (x)
$$\frac{1}{\cos^{2}{\left(x \right)}}$$
1/(cos(x)^2)
Descomposición de una fracción [src]
cos(x)^(-2)
$$\frac{1}{\cos^{2}{\left(x \right)}}$$
   1   
-------
   2   
cos (x)
Potencias [src]
       1       
---------------
              2
/ I*x    -I*x\ 
|e      e    | 
|---- + -----| 
\ 2       2  / 
$$\frac{1}{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}$$
(exp(i*x)/2 + exp(-i*x)/2)^(-2)
Respuesta numérica [src]
cos(x)^(-2)
cos(x)^(-2)
Parte trigonométrica [src]
              2
 /       2/x\\ 
 |1 + cot |-|| 
 \        \2// 
---------------
              2
/        2/x\\ 
|-1 + cot |-|| 
\         \2// 
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}$$
   2/pi    \
csc |-- - x|
    \2     /
$$\csc^{2}{\left(- x + \frac{\pi}{2} \right)}$$
        2        
-----------------
       /pi      \
1 + sin|-- + 2*x|
       \2       /
$$\frac{2}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1}$$
     2      
------------
1 + cos(2*x)
$$\frac{2}{\cos{\left(2 x \right)} + 1}$$
   2   
sec (x)
$$\sec^{2}{\left(x \right)}$$
             2
/       2/x\\ 
|1 + tan |-|| 
\        \2// 
--------------
             2
/       2/x\\ 
|1 - tan |-|| 
\        \2// 
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}$$
       2       
---------------
           2   
    1 - tan (x)
1 + -----------
           2   
    1 + tan (x)
$$\frac{2}{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1}$$
     1      
------------
   2/    pi\
sin |x + --|
    \    2 /
$$\frac{1}{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}$$
     2      
------------
       1    
1 + --------
    sec(2*x)
$$\frac{2}{1 + \frac{1}{\sec{\left(2 x \right)}}}$$
       2        
----------------
            2   
    -1 + cot (x)
1 + ------------
           2    
    1 + cot (x) 
$$\frac{2}{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1}$$
        2        
-----------------
          1      
1 + -------------
       /pi      \
    csc|-- - 2*x|
       \2       /
$$\frac{2}{1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}}$$
2/(1 + 1/csc(pi/2 - 2*x))