Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   2         1    
cot (x) - --------
          cos(2*x)
cot⁡2(x)−1cos⁡(2x)\cot^{2}{\left(x \right)} - \frac{1}{\cos{\left(2 x \right)}} 
cot(x)^2 - 1/cos(2*x)
Simplificación general [src] 
   1         1    
------- - --------
   2      cos(2*x)
tan (x)
1tan⁡2(x)−1cos⁡(2x)\frac{1}{\tan^{2}{\left(x \right)}} - \frac{1}{\cos{\left(2 x \right)}} 
tan(x)^(-2) - 1/cos(2*x)
Respuesta numérica [src] 
cot(x)^2 - 1/cos(2*x)
cot(x)^2 - 1/cos(2*x)
Combinatoria [src] 
        2            
-1 + cot (x)*cos(2*x)
---------------------
       cos(2*x)
cos⁡(2x)cot⁡2(x)−1cos⁡(2x)\frac{\cos{\left(2 x \right)} \cot^{2}{\left(x \right)} - 1}{\cos{\left(2 x \right)}} 
(-1 + cot(x)^2*cos(2*x))/cos(2*x)
Potencias [src] 
   2             1        
cot (x) - ----------------
           -2*I*x    2*I*x
          e         e     
          ------- + ------
             2        2
cot⁡2(x)−1e2ix2+e−2ix2\cot^{2}{\left(x \right)} - \frac{1}{\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}} 
cot(x)^2 - 1/(exp(-2*i*x)/2 + exp(2*i*x)/2)
Unión de expresiones racionales [src] 
        2            
-1 + cot (x)*cos(2*x)
---------------------
       cos(2*x)
cos⁡(2x)cot⁡2(x)−1cos⁡(2x)\frac{\cos{\left(2 x \right)} \cot^{2}{\left(x \right)} - 1}{\cos{\left(2 x \right)}} 
(-1 + cot(x)^2*cos(2*x))/cos(2*x)
Denominador racional [src] 
        2            
-1 + cot (x)*cos(2*x)
---------------------
       cos(2*x)
cos⁡(2x)cot⁡2(x)−1cos⁡(2x)\frac{\cos{\left(2 x \right)} \cot^{2}{\left(x \right)} - 1}{\cos{\left(2 x \right)}} 
(-1 + cot(x)^2*cos(2*x))/cos(2*x)
Parte trigonométrica [src] 
   1              
------- - sec(2*x)
   2              
tan (x)
−sec⁡(2x)+1tan⁡2(x)- \sec{\left(2 x \right)} + \frac{1}{\tan^{2}{\left(x \right)}} 
                       2      
     /pi      \     csc (x)   
- csc|-- - 2*x| + ------------
     \2       /      2/pi    \
                  csc |-- - x|
                      \2     /
csc⁡2(x)csc⁡2(−x+π2)−csc⁡(−2x+π2)\frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - \csc{\left(- 2 x + \frac{\pi}{2} \right)} 
                     2     
        1         sin (2*x)
- ------------- + ---------
     /pi      \        4   
  sin|-- + 2*x|   4*sin (x)
     \2       /
−1sin⁡(2x+π2)+sin⁡2(2x)4sin⁡4(x)- \frac{1}{\sin{\left(2 x + \frac{\pi}{2} \right)}} + \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}} 
                2   
     1       cos (x)
- -------- + -------
  cos(2*x)      2   
             sin (x)
−1cos⁡(2x)+cos⁡2(x)sin⁡2(x)- \frac{1}{\cos{\left(2 x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} 
                  2      
     1         cos (x)   
- -------- + ------------
  cos(2*x)      2/    pi\
             cos |x - --|
                 \    2 /
cos⁡2(x)cos⁡2(x−π2)−1cos⁡(2x)\frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{\cos{\left(2 x \right)}} 
               2   
            csc (x)
-sec(2*x) + -------
               2   
            sec (x)
csc⁡2(x)sec⁡2(x)−sec⁡(2x)\frac{\csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} - \sec{\left(2 x \right)} 
   1         1    
------- - --------
   2      cos(2*x)
tan (x)
1tan⁡2(x)−1cos⁡(2x)\frac{1}{\tan^{2}{\left(x \right)}} - \frac{1}{\cos{\left(2 x \right)}} 
                2     
     1       sin (2*x)
- -------- + ---------
  cos(2*x)        4   
             4*sin (x)
−1cos⁡(2x)+sin⁡2(2x)4sin⁡4(x)- \frac{1}{\cos{\left(2 x \right)}} + \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}} 
                 2   
   1      1 + tan (x)
------- - -----------
   2             2   
tan (x)   1 - tan (x)
1tan⁡2(x)−tan⁡2(x)+11−tan⁡2(x)\frac{1}{\tan^{2}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{1 - \tan^{2}{\left(x \right)}} 
                 2    
   2      1 + cot (x) 
cot (x) - ------------
                  2   
          -1 + cot (x)
cot⁡2(x)−cot⁡2(x)+1cot⁡2(x)−1\cot^{2}{\left(x \right)} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot^{2}{\left(x \right)} - 1} 
               2/    pi\
            sec |x - --|
                \    2 /
-sec(2*x) + ------------
                 2      
              sec (x)
−sec⁡(2x)+sec⁡2(x−π2)sec⁡2(x)- \sec{\left(2 x \right)} + \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}} 
-sec(2*x) + sec(x - pi/2)^2/sec(x)^2
Abrimos la expresión [src] 
   2            1       
cot (x) - --------------
                    2   
          -1 + 2*cos (x)
cot⁡2(x)−12cos⁡2(x)−1\cot^{2}{\left(x \right)} - \frac{1}{2 \cos^{2}{\left(x \right)} - 1} 
cot(x)^2 - 1/(-1 + 2*cos(x)^2)
    © Sr Examen – Калькулятор