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(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
y/(y-3)+3/(3-y)
((z^2-z)/(z^2-9))^-1/((z^2-3*z)/(z-1))
(a^(7*a))^2/(-a)^15
Factorizar el polinomio:
y^x*y^3-y-1+y^x*y
y^8-1
y^4+y^3
y^3-x*y^2+y-x
Descomponer al cuadrado:
y^4-8*y^2-9
-y^4-8*y^2+7
-y^4+8*y^2+3
y^4-9*y^2+15
Expresiones idénticas
tan(t)/(uno -tan(t)^(dos))+cot(t)/(uno -cot(t)^(dos))
tangente de (t) dividir por (1 menos tangente de (t) en el grado (2)) más cotangente de (t) dividir por (1 menos cotangente de (t) en el grado (2))
tangente de (t) dividir por (uno menos tangente de (t) en el grado (dos)) más cotangente de (t) dividir por (uno menos cotangente de (t) en el grado (dos))
tan(t)/(1-tan(t)(2))+cot(t)/(1-cot(t)(2))
tant/1-tant2+cott/1-cott2
tant/1-tant^2+cott/1-cott^2
tan(t) dividir por (1-tan(t)^(2))+cot(t) dividir por (1-cot(t)^(2))
Expresiones semejantes
tan(t)/(1-tan(t)^(2))-cot(t)/(1-cot(t)^(2))
tan(t)/(1-tan(t)^(2))+cot(t)/(1+cot(t)^(2))
tan(t)/(1+tan(t)^(2))+cot(t)/(1-cot(t)^(2))
Expresiones con funciones
Tangente tan
tan(x)/(2*tan(x)^2+2)+x/2
tan(x)/(2*tan(x)^2+2)+tan(x)-(3*x)/2
tan(x/4+pi/8)/2-1/(2*tan(x/4+pi/8))
tan(x)/(1-tan(x)^(2))+cot(x)/(1-cot(x)^(2))
tan(pi/8)/(2-2*tan(pi/8)^(2))
Tangente tan
tan(x)/(2*tan(x)^2+2)+x/2
tan(x)/(2*tan(x)^2+2)+tan(x)-(3*x)/2
tan(x/4+pi/8)/2-1/(2*tan(x/4+pi/8))
tan(x)/(1-tan(x)^(2))+cot(x)/(1-cot(x)^(2))
tan(pi/8)/(2-2*tan(pi/8)^(2))
Cotangente cot
cot(x)^2*((2+2*tan(x)^2)*tan(x)/cot(x)^2-tan(x)^2*(-2-2*cot(x)^2)/cot(x)^3)/(2*tan(x)^2)
cot(x^2/2+pi/3)/(-1+cot(x^2/2+pi/3)^2)
Cotangente cot
cot(x)^2*((2+2*tan(x)^2)*tan(x)/cot(x)^2-tan(x)^2*(-2-2*cot(x)^2)/cot(x)^3)/(2*tan(x)^2)
cot(x^2/2+pi/3)/(-1+cot(x^2/2+pi/3)^2)

Simplificación de expresiones/ Descomposición en fracciones simples/ tan(t)/(1-tan(t)^(2))+cot(t)/(1-cot(t)^(2))

¿Cómo vas a descomponer esta tan(t)/(1-tan(t)^(2))+cot(t)/(1-cot(t)^(2)) expresión en fracciones?

Solución

Ha introducido [src]

   tan(t)        cot(t)  
----------- + -----------
       2             2   
1 - tan (t)   1 - cot (t)

\frac{\cot{\left(t \right)}}{1 - \cot^{2}{\left(t \right)}} + \frac{\tan{\left(t \right)}}{1 - \tan^{2}{\left(t \right)}}

tan(t)/(1 - tan(t)^2) + cot(t)/(1 - cot(t)^2)

Simplificación general [src]

0

Respuesta numérica [src]

cot(t)/(1.0 - cot(t)^2) + tan(t)/(1.0 - tan(t)^2)

cot(t)/(1.0 - cot(t)^2) + tan(t)/(1.0 - tan(t)^2)

Denominador común [src]

 /                      2                2          \ 
-\-cot(t) - tan(t) + cot (t)*tan(t) + tan (t)*cot(t)/ 
------------------------------------------------------
              2         2         2       2           
       1 - cot (t) - tan (t) + cot (t)*tan (t)

- \frac{\tan^{2}{\left(t \right)} \cot{\left(t \right)} + \tan{\left(t \right)} \cot^{2}{\left(t \right)} - \tan{\left(t \right)} - \cot{\left(t \right)}}{\tan^{2}{\left(t \right)} \cot^{2}{\left(t \right)} - \tan^{2}{\left(t \right)} - \cot^{2}{\left(t \right)} + 1}

-(-cot(t) - tan(t) + cot(t)^2*tan(t) + tan(t)^2*cot(t))/(1 - cot(t)^2 - tan(t)^2 + cot(t)^2*tan(t)^2)

Potencias [src]

                          /   I*t    -I*t\          
   cot(t)               I*\- e    + e    /          
----------- + --------------------------------------
       2      /                    2\               
1 - cot (t)   |    /   I*t    -I*t\ |               
              |    \- e    + e    / | / I*t    -I*t\
              |1 + -----------------|*\e    + e    /
              |                   2 |               
              |     / I*t    -I*t\  |               
              \     \e    + e    /  /

\frac{i \left(- e^{i t} + e^{- i t}\right)}{\left(\frac{\left(- e^{i t} + e^{- i t}\right)^{2}}{\left(e^{i t} + e^{- i t}\right)^{2}} + 1\right) \left(e^{i t} + e^{- i t}\right)} + \frac{\cot{\left(t \right)}}{1 - \cot^{2}{\left(t \right)}}

cot(t)/(1 - cot(t)^2) + i*(-exp(i*t) + exp(-i*t))/((1 + (-exp(i*t) + exp(-i*t))^2/(exp(i*t) + exp(-i*t))^2)*(exp(i*t) + exp(-i*t)))

Unión de expresiones racionales [src]

/       2   \          /       2   \       
\1 - cot (t)/*tan(t) + \1 - tan (t)/*cot(t)
-------------------------------------------
        /       2   \ /       2   \        
        \1 - cot (t)/*\1 - tan (t)/

\frac{\left(1 - \tan^{2}{\left(t \right)}\right) \cot{\left(t \right)} + \left(1 - \cot^{2}{\left(t \right)}\right) \tan{\left(t \right)}}{\left(1 - \tan^{2}{\left(t \right)}\right) \left(1 - \cot^{2}{\left(t \right)}\right)}

((1 - cot(t)^2)*tan(t) + (1 - tan(t)^2)*cot(t))/((1 - cot(t)^2)*(1 - tan(t)^2))

Combinatoria [src]

       -(-1 + cot(t)*tan(t))*(cot(t) + tan(t))       
-----------------------------------------------------
(1 + cot(t))*(1 + tan(t))*(-1 + cot(t))*(-1 + tan(t))

- \frac{\left(\tan{\left(t \right)} \cot{\left(t \right)} - 1\right) \left(\tan{\left(t \right)} + \cot{\left(t \right)}\right)}{\left(\tan{\left(t \right)} - 1\right) \left(\tan{\left(t \right)} + 1\right) \left(\cot{\left(t \right)} - 1\right) \left(\cot{\left(t \right)} + 1\right)}

-(-1 + cot(t)*tan(t))*(cot(t) + tan(t))/((1 + cot(t))*(1 + tan(t))*(-1 + cot(t))*(-1 + tan(t)))

Parte trigonométrica [src]

     /pi      \                             
  csc|-- - 2*t|                             
     \2       /           2*csc(2*t)        
- ------------- + --------------------------
    2*csc(2*t)    /       2/pi    \\        
                  |    csc |-- - t||        
                  |        \2     /|    2   
                  |1 - ------------|*csc (t)
                  |         2      |        
                  \      csc (t)   /

- \frac{\csc{\left(- 2 t + \frac{\pi}{2} \right)}}{2 \csc{\left(2 t \right)}} + \frac{2 \csc{\left(2 t \right)}}{\left(1 - \frac{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}}{\csc^{2}{\left(t \right)}}\right) \csc^{2}{\left(t \right)}}

                                        2           
         sin(2*t)                  2*sin (t)        
------------------------- + ------------------------
  /       2     \           /         4   \         
  |    sin (2*t)|    2      |    4*sin (t)|         
2*|1 - ---------|*sin (t)   |1 - ---------|*sin(2*t)
  |         4   |           |       2     |         
  \    4*sin (t)/           \    sin (2*t)/

\frac{2 \sin^{2}{\left(t \right)}}{\left(- \frac{4 \sin^{4}{\left(t \right)}}{\sin^{2}{\left(2 t \right)}} + 1\right) \sin{\left(2 t \right)}} + \frac{\sin{\left(2 t \right)}}{2 \left(1 - \frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{4}{\left(t \right)}}\right) \sin^{2}{\left(t \right)}}

         1                tan(t)  
-------------------- + -----------
/       1   \                 2   
|1 - -------|*tan(t)   1 - tan (t)
|       2   |                     
\    tan (t)/

\frac{\tan{\left(t \right)}}{1 - \tan^{2}{\left(t \right)}} + \frac{1}{\left(1 - \frac{1}{\tan^{2}{\left(t \right)}}\right) \tan{\left(t \right)}}

                  2            
  tan(2*t)   2*sin (t)*csc(2*t)
- -------- + ------------------
     2                 2       
                1 - tan (t)

- \frac{\tan{\left(2 t \right)}}{2} + \frac{2 \sin^{2}{\left(t \right)} \csc{\left(2 t \right)}}{1 - \tan^{2}{\left(t \right)}}

         1                cot(t)  
-------------------- + -----------
/       1   \                 2   
|1 - -------|*cot(t)   1 - cot (t)
|       2   |                     
\    cot (t)/

\frac{\cot{\left(t \right)}}{1 - \cot^{2}{\left(t \right)}} + \frac{1}{\left(1 - \frac{1}{\cot^{2}{\left(t \right)}}\right) \cot{\left(t \right)}}

                        2          
  tan(2*t)         2*sin (t)       
- -------- + ----------------------
     2       /       2   \         
             \1 - tan (t)/*sin(2*t)

- \frac{\tan{\left(2 t \right)}}{2} + \frac{2 \sin^{2}{\left(t \right)}}{\left(1 - \tan^{2}{\left(t \right)}\right) \sin{\left(2 t \right)}}

                                 /      pi\        
                            2*sec|2*t - --|        
      sec(2*t)                   \      2 /        
- --------------- + -------------------------------
       /      pi\   /         2      \             
  2*sec|2*t - --|   |      sec (t)   |    2/    pi\
       \      2 /   |1 - ------------|*sec |t - --|
                    |       2/    pi\|     \    2 /
                    |    sec |t - --||             
                    \        \    2 //

- \frac{\sec{\left(2 t \right)}}{2 \sec{\left(2 t - \frac{\pi}{2} \right)}} + \frac{2 \sec{\left(2 t - \frac{\pi}{2} \right)}}{\left(- \frac{\sec^{2}{\left(t \right)}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(t - \frac{\pi}{2} \right)}}

       sin(t)                 cos(t)       
-------------------- + --------------------
/       2   \          /       2   \       
|    sin (t)|          |    cos (t)|       
|1 - -------|*cos(t)   |1 - -------|*sin(t)
|       2   |          |       2   |       
\    cos (t)/          \    sin (t)/

\frac{\sin{\left(t \right)}}{\left(- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \cos{\left(t \right)}} + \frac{\cos{\left(t \right)}}{\left(1 - \frac{\cos^{2}{\left(t \right)}}{\sin^{2}{\left(t \right)}}\right) \sin{\left(t \right)}}

                          2/t\ /       2   \      
                     4*cot |-|*\1 + cot (t)/      
      1                    \2/                    
- ---------- + -----------------------------------
  2*cot(2*t)                2                     
               /       2/t\\  /       1   \       
               |1 + cot |-|| *|1 - -------|*cot(t)
               \        \2//  |       2   |       
                              \    cot (t)/

- \frac{1}{2 \cot{\left(2 t \right)}} + \frac{4 \left(\cot^{2}{\left(t \right)} + 1\right) \cot^{2}{\left(\frac{t}{2} \right)}}{\left(1 - \frac{1}{\cot^{2}{\left(t \right)}}\right) \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2} \cot{\left(t \right)}}

                        2/t\ /       2   \      
                   4*tan |-|*\1 + tan (t)/      
  tan(2*t)               \2/                    
- -------- + -----------------------------------
     2                    2                     
             /       2/t\\  /       2   \       
             |1 + tan |-|| *\1 - tan (t)/*tan(t)
             \        \2//

- \frac{\tan{\left(2 t \right)}}{2} + \frac{4 \left(\tan^{2}{\left(t \right)} + 1\right) \tan^{2}{\left(\frac{t}{2} \right)}}{\left(1 - \tan^{2}{\left(t \right)}\right) \left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2} \tan{\left(t \right)}}

     2                    2           
  sin (2*t)          2*sin (t)        
- --------- + ------------------------
   sin(4*t)   /         4   \         
              |    4*sin (t)|         
              |1 - ---------|*sin(2*t)
              |       2     |         
              \    sin (2*t)/

- \frac{\sin^{2}{\left(2 t \right)}}{\sin{\left(4 t \right)}} + \frac{2 \sin^{2}{\left(t \right)}}{\left(- \frac{4 \sin^{4}{\left(t \right)}}{\sin^{2}{\left(2 t \right)}} + 1\right) \sin{\left(2 t \right)}}

          /    pi\                                        
       sec|t - --|                                        
          \    2 /                      sec(t)            
------------------------- + ------------------------------
/       2/    pi\\          /         2      \            
|    sec |t - --||          |      sec (t)   |    /    pi\
|        \    2 /|          |1 - ------------|*sec|t - --|
|1 - ------------|*sec(t)   |       2/    pi\|    \    2 /
|         2      |          |    sec |t - --||            
\      sec (t)   /          \        \    2 //

\frac{\sec{\left(t \right)}}{\left(- \frac{\sec^{2}{\left(t \right)}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(t - \frac{\pi}{2} \right)}} + \frac{\sec{\left(t - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\sec^{2}{\left(t \right)}}\right) \sec{\left(t \right)}}

0

     /      pi\                 2/    pi\         
  cos|2*t - --|            2*cos |t - --|         
     \      2 /                  \    2 /         
- ------------- + --------------------------------
    2*cos(2*t)    /       2/    pi\\              
                  |    cos |t - --||              
                  |        \    2 /|    /      pi\
                  |1 - ------------|*cos|2*t - --|
                  |         2      |    \      2 /
                  \      cos (t)   /

- \frac{\cos{\left(2 t - \frac{\pi}{2} \right)}}{2 \cos{\left(2 t \right)}} + \frac{2 \cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t \right)}}\right) \cos{\left(2 t - \frac{\pi}{2} \right)}}

          /pi    \                                        
       csc|-- - t|                                        
          \2     /                      csc(t)            
------------------------- + ------------------------------
/       2/pi    \\          /         2      \            
|    csc |-- - t||          |      csc (t)   |    /pi    \
|        \2     /|          |1 - ------------|*csc|-- - t|
|1 - ------------|*csc(t)   |       2/pi    \|    \2     /
|         2      |          |    csc |-- - t||            
\      csc (t)   /          \        \2     //

\frac{\csc{\left(t \right)}}{\left(- \frac{\csc^{2}{\left(t \right)}}{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- t + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- t + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}}{\csc^{2}{\left(t \right)}}\right) \csc{\left(t \right)}}

       sec(t)                 csc(t)       
-------------------- + --------------------
/       2   \          /       2   \       
|    sec (t)|          |    csc (t)|       
|1 - -------|*csc(t)   |1 - -------|*sec(t)
|       2   |          |       2   |       
\    csc (t)/          \    sec (t)/

\frac{\csc{\left(t \right)}}{\left(- \frac{\csc^{2}{\left(t \right)}}{\sec^{2}{\left(t \right)}} + 1\right) \sec{\left(t \right)}} + \frac{\sec{\left(t \right)}}{\left(1 - \frac{\sec^{2}{\left(t \right)}}{\csc^{2}{\left(t \right)}}\right) \csc{\left(t \right)}}

          /    pi\                                        
       cos|t - --|                                        
          \    2 /                      cos(t)            
------------------------- + ------------------------------
/       2/    pi\\          /         2      \            
|    cos |t - --||          |      cos (t)   |    /    pi\
|        \    2 /|          |1 - ------------|*cos|t - --|
|1 - ------------|*cos(t)   |       2/    pi\|    \    2 /
|         2      |          |    cos |t - --||            
\      cos (t)   /          \        \    2 //

\frac{\cos{\left(t \right)}}{\left(- \frac{\cos^{2}{\left(t \right)}}{\cos^{2}{\left(t - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(t - \frac{\pi}{2} \right)}} + \frac{\cos{\left(t - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t \right)}}\right) \cos{\left(t \right)}}

cos(t - pi/2)/((1 - cos(t - pi/2)^2/cos(t)^2)*cos(t)) + cos(t)/((1 - cos(t)^2/cos(t - pi/2)^2)*cos(t - pi/2))

Denominador racional [src]

/       2   \          /       2   \       
\1 - cot (t)/*tan(t) + \1 - tan (t)/*cot(t)
-------------------------------------------
        /       2   \ /       2   \        
        \1 - cot (t)/*\1 - tan (t)/

\frac{\left(1 - \tan^{2}{\left(t \right)}\right) \cot{\left(t \right)} + \left(1 - \cot^{2}{\left(t \right)}\right) \tan{\left(t \right)}}{\left(1 - \tan^{2}{\left(t \right)}\right) \left(1 - \cot^{2}{\left(t \right)}\right)}

((1 - cot(t)^2)*tan(t) + (1 - tan(t)^2)*cot(t))/((1 - cot(t)^2)*(1 - tan(t)^2))

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta tan(t)/(1-tan(t)^(2))+cot(t)/(1-cot(t)^(2)) expresión en fracciones?

Solución