Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
       2                                  
    cos (x)       sin(x) + cos(x)   sin(x)
--------------- - --------------- + ------
sin(x) - cos(x)            2        tan(x)
                    1 - cot (x)
$$\left(\frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}\right) + \frac{\sin{\left(x \right)}}{\tan{\left(x \right)}}$$ 
cos(x)^2/(sin(x) - cos(x)) - (sin(x) + cos(x))/(1 - cot(x)^2) + sin(x)/tan(x)
Simplificación general [src] 
  ___ /         2        ___           /    pi\\    /    pi\
\/ 2 *|1 - 2*cos (x) + \/ 2 *cos(x)*sin|x + --||*cos|x + --|
      \                                \    4 //    \    4 /
------------------------------------------------------------
                        2         2                         
                     sin (x) - cos (x)
$$\frac{\sqrt{2} \left(\sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)} \cos{\left(x \right)} - 2 \cos^{2}{\left(x \right)} + 1\right) \cos{\left(x + \frac{\pi}{4} \right)}}{\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}$$ 
sqrt(2)*(1 - 2*cos(x)^2 + sqrt(2)*cos(x)*sin(x + pi/4))*cos(x + pi/4)/(sin(x)^2 - cos(x)^2)
Compilar la expresión [src] 
       2                                   
    cos (x)        sin(x)   cos(x) + sin(x)
---------------- + ------ - ---------------
-cos(x) + sin(x)   tan(x)            2     
                              1 - cot (x)
$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$ 
cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x) - (cos(x) + sin(x))/(1 - cot(x)^2)
Abrimos la expresión [src] 
       2                                            
    cos (x)       sin(x)      cos(x)        sin(x)  
--------------- + ------ - ----------- - -----------
sin(x) - cos(x)   tan(x)          2             2   
                           1 - cot (x)   1 - cot (x)
$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}} - \frac{\cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$ 
cos(x)^2/(sin(x) - cos(x)) + sin(x)/tan(x) - cos(x)/(1 - cot(x)^2) - sin(x)/(1 - cot(x)^2)
Potencias [src] 
       2                                   
    cos (x)        sin(x)   cos(x) + sin(x)
---------------- + ------ - ---------------
-cos(x) + sin(x)   tan(x)            2     
                              1 - cot (x)
$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} - \frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$ 
                          2                 
-cos(x) - sin(x)       cos (x)        sin(x)
---------------- + ---------------- + ------
         2         -cos(x) + sin(x)   tan(x)
  1 - cot (x)
$$\frac{\sin{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}} + \frac{- \sin{\left(x \right)} - \cos{\left(x \right)}}{1 - \cot^{2}{\left(x \right)}}$$ 
                        2                                                                                
          / I*x    -I*x\               I*x    -I*x     /   -I*x    I*x\                                  
          |e      e    |              e      e       I*\- e     + e   /                                  
          |---- + -----|              ---- + ----- - ------------------   /   -I*x    I*x\ / I*x    -I*x\
          \ 2       2  /               2       2             2            \- e     + e   /*\e    + e    /
----------------------------------- - --------------------------------- - -------------------------------
   I*x    -I*x     /   -I*x    I*x\                     2                          /   I*x    -I*x\      
  e      e       I*\- e     + e   /              1 - cot (x)                     2*\- e    + e    /      
- ---- - ----- - ------------------                                                                      
   2       2             2
$$\frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} - \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}} - \frac{\left(e^{i x} - e^{- i x}\right) \left(e^{i x} + e^{- i x}\right)}{2 \left(- e^{i x} + e^{- i x}\right)} - \frac{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + \frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{1 - \cot^{2}{\left(x \right)}}$$ 
(exp(i*x)/2 + exp(-i*x)/2)^2/(-exp(i*x)/2 - exp(-i*x)/2 - i*(-exp(-i*x) + exp(i*x))/2) - (exp(i*x)/2 + exp(-i*x)/2 - i*(-exp(-i*x) + exp(i*x))/2)/(1 - cot(x)^2) - (-exp(-i*x) + exp(i*x))*(exp(i*x) + exp(-i*x))/(2*(-exp(i*x) + exp(-i*x)))
Combinatoria [src] 
 /     2         2       2         2                                  2                2       2                2                 \ 
-\- sin (x) + cot (x)*sin (x) + sin (x)*tan(x) + cos(x)*sin(x) - 2*cos (x)*tan(x) + cos (x)*cot (x)*tan(x) - cot (x)*cos(x)*sin(x)/ 
------------------------------------------------------------------------------------------------------------------------------------
                                        (1 + cot(x))*(-1 + cot(x))*(-sin(x) + cos(x))*tan(x)
$$- \frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)} + \sin^{2}{\left(x \right)} \cot^{2}{\left(x \right)} - \sin^{2}{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} \cot^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\cot{\left(x \right)} - 1\right) \left(\cot{\left(x \right)} + 1\right) \tan{\left(x \right)}}$$ 
-(-sin(x)^2 + cot(x)^2*sin(x)^2 + sin(x)^2*tan(x) + cos(x)*sin(x) - 2*cos(x)^2*tan(x) + cos(x)^2*cot(x)^2*tan(x) - cot(x)^2*cos(x)*sin(x))/((1 + cot(x))*(-1 + cot(x))*(-sin(x) + cos(x))*tan(x))
Unión de expresiones racionales [src] 
/   2    /       2   \                                       \          /       2   \                          
\cos (x)*\1 - cot (x)/ - (-cos(x) + sin(x))*(cos(x) + sin(x))/*tan(x) + \1 - cot (x)/*(-cos(x) + sin(x))*sin(x)
---------------------------------------------------------------------------------------------------------------
                                    /       2   \                                                              
                                    \1 - cot (x)/*(-cos(x) + sin(x))*tan(x)
$$\frac{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} + \left(\left(1 - \cot^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} - \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)\right) \tan{\left(x \right)}}{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \tan{\left(x \right)}}$$ 
((cos(x)^2*(1 - cot(x)^2) - (-cos(x) + sin(x))*(cos(x) + sin(x)))*tan(x) + (1 - cot(x)^2)*(-cos(x) + sin(x))*sin(x))/((1 - cot(x)^2)*(-cos(x) + sin(x))*tan(x))
Respuesta numérica [src] 
cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x) - (cos(x) + sin(x))/(1.0 - cot(x)^2)
cos(x)^2/(-cos(x) + sin(x)) + sin(x)/tan(x) - (cos(x) + sin(x))/(1.0 - cot(x)^2)
Denominador racional [src] 
/   2    /       2   \                                        \          /       2   \                          
\cos (x)*\1 - cot (x)/ + (-cos(x) - sin(x))*(-cos(x) + sin(x))/*tan(x) + \1 - cot (x)/*(-cos(x) + sin(x))*sin(x)
----------------------------------------------------------------------------------------------------------------
                                    /       2   \                                                               
                                    \1 - cot (x)/*(-cos(x) + sin(x))*tan(x)
$$\frac{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} + \left(\left(1 - \cot^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} + \left(- \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \tan{\left(x \right)}}{\left(1 - \cot^{2}{\left(x \right)}\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \tan{\left(x \right)}}$$ 
((cos(x)^2*(1 - cot(x)^2) + (-cos(x) - sin(x))*(-cos(x) + sin(x)))*tan(x) + (1 - cot(x)^2)*(-cos(x) + sin(x))*sin(x))/((1 - cot(x)^2)*(-cos(x) + sin(x))*tan(x))
Denominador común [src] 
                      2         2                2       2                         2                       2       2          
                   sin (x) + cos (x)*tan(x) - cot (x)*sin (x) - cos(x)*sin(x) + cot (x)*cos(x)*sin(x) - cot (x)*sin (x)*tan(x)
-cos(x) - sin(x) + -----------------------------------------------------------------------------------------------------------
                                                                     2                       2                                
                                  sin(x)*tan(x) - cos(x)*tan(x) + cot (x)*cos(x)*tan(x) - cot (x)*sin(x)*tan(x)
$$- \sin{\left(x \right)} - \cos{\left(x \right)} + \frac{- \sin^{2}{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} - \sin^{2}{\left(x \right)} \cot^{2}{\left(x \right)} + \sin^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} \cot^{2}{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{- \sin{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} + \sin{\left(x \right)} \tan{\left(x \right)} + \cos{\left(x \right)} \tan{\left(x \right)} \cot^{2}{\left(x \right)} - \cos{\left(x \right)} \tan{\left(x \right)}}$$ 
-cos(x) - sin(x) + (sin(x)^2 + cos(x)^2*tan(x) - cot(x)^2*sin(x)^2 - cos(x)*sin(x) + cot(x)^2*cos(x)*sin(x) - cot(x)^2*sin(x)^2*tan(x))/(sin(x)*tan(x) - cos(x)*tan(x) + cot(x)^2*cos(x)*tan(x) - cot(x)^2*sin(x)*tan(x))
    © Sr Examen – Калькулятор