Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
¿cómo vas a descomponer esta expresión en fracciones?:
((z-2)/(4*(z+2)^2))/(z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z))
x^3*y^12/(x*y^4)^3
(((z/(1+z*v))/(1+(z/(1+z*v)))))*y*((1/(1-1*u*x)))*(x-t)
2*(-1+(-1+x)/(2+x))/(2+x)^2
Factorizar el polinomio:
y^5-y^3-y+1
y^5+y+1
-y^3+y^2-1
y^3+y^2*x-3*y*x+9*x+27
Descomponer al cuadrado:
-y^4-8*y^2-8
-y^4+9*y^2-3
-y^4+8*y^2+4
-y^4+8*y^2+8
Expresiones idénticas
sin dos 0/(2*cos10)
seno de 20 dividir por (2 multiplicar por coseno de 10)
seno de dos 0 dividir por (2 multiplicar por coseno de 10)
sin20/(2cos10)
sin20/2cos10
sin20 dividir por (2*cos10)

Simplificación de expresiones/ Descomposición en fracciones simples/ sin20/(2*cos10)

¿Cómo vas a descomponer esta sin20/(2*cos10) expresión en fracciones?

Solución

Ha introducido [src]

 sin(20) 
---------
2*cos(10)

$$\frac{\sin{\left(20 \right)}}{2 \cos{\left(10 \right)}}$$

sin(20)/((2*cos(10)))

Simplificación general [src]

sin(10)

$$\sin{\left(10 \right)}$$

sin(10)

Potencias [src]

   /   -20*I    20*I\ 
-I*\- e      + e    / 
----------------------
    / -10*I    10*I\  
  2*\e      + e    /

$$- \frac{i \left(- e^{- 20 i} + e^{20 i}\right)}{2 \left(e^{10 i} + e^{- 10 i}\right)}$$

-i*(-exp(-20*i) + exp(20*i))/(2*(exp(-10*i) + exp(10*i)))

Abrimos la expresión [src]

                                      15                                                                           11                                                                           19                                                                           7                                                                           3                                                                                                                                                          5                                                                            9                                                                            17                                                                           13                                    
                           2228224*sin  (1)*cos(1)                                                      1397760*sin  (1)*cos(1)                                                       262144*sin  (1)*cos(1)                                                       109824*sin (1)*cos(1)                                                          660*sin (1)*cos(1)                                                            10*cos(1)*sin(1)                                                           12672*sin (1)*cos(1)                                                        512512*sin (1)*cos(1)                                                       1179648*sin  (1)*cos(1)                                                      2293760*sin  (1)*cos(1)                          
- -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- + -------------------------------------------------------------------------- + -------------------------------------------------------------------------- + -------------------------------------------------------------------------- + -------------------------------------------------------------------------- + --------------------------------------------------------------------------
               8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6                   8             4            2             10              6   
  -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)   -1 - 1280*cos (1) - 400*cos (1) + 50*cos (1) + 512*cos  (1) + 1120*cos (1)

$$\frac{2293760 \sin^{13}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} + \frac{512512 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} + \frac{1179648 \sin^{17}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} + \frac{12672 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} + \frac{10 \sin{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} - \frac{660 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} - \frac{262144 \sin^{19}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} - \frac{109824 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} - \frac{2228224 \sin^{15}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}} - \frac{1397760 \sin^{11}{\left(1 \right)} \cos{\left(1 \right)}}{- 400 \cos^{4}{\left(1 \right)} - 1280 \cos^{8}{\left(1 \right)} - 1 + 512 \cos^{10}{\left(1 \right)} + 50 \cos^{2}{\left(1 \right)} + 1120 \cos^{6}{\left(1 \right)}}$$

-2228224*sin(1)^15*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) - 1397760*sin(1)^11*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) - 262144*sin(1)^19*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) - 109824*sin(1)^7*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) - 660*sin(1)^3*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) + 10*cos(1)*sin(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) + 12672*sin(1)^5*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) + 512512*sin(1)^9*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) + 1179648*sin(1)^17*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6) + 2293760*sin(1)^13*cos(1)/(-1 - 1280*cos(1)^8 - 400*cos(1)^4 + 50*cos(1)^2 + 512*cos(1)^10 + 1120*cos(1)^6)

Parte trigonométrica [src]

     1      
------------
   /     pi\
sec|10 - --|
   \     2 /

$$\frac{1}{\sec{\left(10 - \frac{\pi}{2} \right)}}$$

              tan(10)               
------------------------------------
/       2    \ /       2   \    2   
\1 + tan (10)/*\1 - tan (5)/*cos (5)

$$\frac{\tan{\left(10 \right)}}{\left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right) \cos^{2}{\left(5 \right)}}$$

   sin(20)    
--------------
     /     pi\
2*sin|10 + --|
     \     2 /

$$\frac{\sin{\left(20 \right)}}{2 \sin{\left(\frac{\pi}{2} + 10 \right)}}$$

    /       2   \            
    \1 + cot (5)/*cot(10)    
-----------------------------
/       2    \ /        2   \
\1 + cot (10)/*\-1 + cot (5)/

$$\frac{\left(\cot^{2}{\left(5 \right)} + 1\right) \cot{\left(10 \right)}}{\left(-1 + \cot^{2}{\left(5 \right)}\right) \left(1 + \cot^{2}{\left(10 \right)}\right)}$$

 sec(10) 
---------
2*csc(20)

$$\frac{\sec{\left(10 \right)}}{2 \csc{\left(20 \right)}}$$

                           2                         
                      2*sin (10)                     
-----------------------------------------------------
/         4   \ /         4    \                     
|    4*sin (5)| |    4*sin (10)|            2/    pi\
|1 - ---------|*|1 + ----------|*sin(20)*sin |5 + --|
|        2    | |        2     |             \    2 /
\     sin (10)/ \     sin (20) /

$$\frac{2 \sin^{2}{\left(10 \right)}}{\left(- \frac{4 \sin^{4}{\left(5 \right)}}{\sin^{2}{\left(10 \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(10 \right)}}{\sin^{2}{\left(20 \right)}} + 1\right) \sin{\left(20 \right)} \sin^{2}{\left(\frac{\pi}{2} + 5 \right)}}$$

   /     pi\
cos|20 - --|
   \     2 /
------------
 2*cos(10)

$$\frac{\cos{\left(20 - \frac{\pi}{2} \right)}}{2 \cos{\left(10 \right)}}$$

                     2                             
                  sec (5)*sec(10)                  
---------------------------------------------------
/          2      \ /         2      \             
|       sec (10)  | |      sec (5)   |    /     pi\
|1 + -------------|*|1 - ------------|*sec|10 - --|
|       2/     pi\| |       2/    pi\|    \     2 /
|    sec |10 - --|| |    sec |5 - --||             
\        \     2 // \        \    2 //

$$\frac{\sec^{2}{\left(5 \right)} \sec{\left(10 \right)}}{\left(- \frac{\sec^{2}{\left(5 \right)}}{\sec^{2}{\left(5 - \frac{\pi}{2} \right)}} + 1\right) \left(\frac{\sec^{2}{\left(10 \right)}}{\sec^{2}{\left(10 - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(10 - \frac{\pi}{2} \right)}}$$

   1   
-------
csc(10)

$$\frac{1}{\csc{\left(10 \right)}}$$

   /     pi\
cos|10 - --|
   \     2 /

$$\cos{\left(10 - \frac{\pi}{2} \right)}$$

sin(10)

$$\sin{\left(10 \right)}$$

             2/     pi\    /      pi\           
          csc |-5 + --|*csc|-10 + --|           
              \     2 /    \      2 /           
------------------------------------------------
/       2/      pi\\ /       2/     pi\\        
|    csc |-10 + --|| |    csc |-5 + --||        
|        \      2 /| |        \     2 /|        
|1 + --------------|*|1 - -------------|*csc(10)
|          2       | |          2      |        
\       csc (10)   / \       csc (5)   /

$$\frac{\csc{\left(-10 + \frac{\pi}{2} \right)} \csc^{2}{\left(-5 + \frac{\pi}{2} \right)}}{\left(- \frac{\csc^{2}{\left(-5 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(5 \right)}} + 1\right) \left(\frac{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(10 \right)}} + 1\right) \csc{\left(10 \right)}}$$

                        tan(10)                         
--------------------------------------------------------
                                             2          
/       2    \ /       2   \ /        2     \     4     
\1 + tan (10)/*\1 - tan (5)/*\-1 + cot (5/2)/ *sin (5/2)

$$\frac{\tan{\left(10 \right)}}{\left(-1 + \cot^{2}{\left(\frac{5}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right) \sin^{4}{\left(\frac{5}{2} \right)}}$$

  2*tan(5) 
-----------
       2   
1 + tan (5)

$$\frac{2 \tan{\left(5 \right)}}{1 + \tan^{2}{\left(5 \right)}}$$

                  sin(10)                   
--------------------------------------------
/       2    \ /       2   \    2           
\1 + tan (10)/*\1 - tan (5)/*cos (5)*cos(10)

$$\frac{\sin{\left(10 \right)}}{\left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right) \cos^{2}{\left(5 \right)} \cos{\left(10 \right)}}$$

                        /     pi\                     
                     cos|10 - --|                     
                        \     2 /                     
------------------------------------------------------
/       2/     pi\\ /       2/    pi\\                
|    cos |10 - --|| |    cos |5 - --||                
|        \     2 /| |        \    2 /|    2           
|1 + -------------|*|1 - ------------|*cos (5)*cos(10)
|          2      | |         2      |                
\       cos (10)  / \      cos (5)   /

$$\frac{\cos{\left(10 - \frac{\pi}{2} \right)}}{\left(- \frac{\cos^{2}{\left(5 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(5 \right)}} + 1\right) \left(\frac{\cos^{2}{\left(10 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(10 \right)}} + 1\right) \cos^{2}{\left(5 \right)} \cos{\left(10 \right)}}$$

                        2                       
                   2*sin (10)                   
------------------------------------------------
/         4   \ /         4    \                
|    4*sin (5)| |    4*sin (10)|    2           
|1 - ---------|*|1 + ----------|*cos (5)*sin(20)
|        2    | |        2     |                
\     sin (10)/ \     sin (20) /

   /      pi\
csc|-10 + --|
   \      2 /
-------------
  2*csc(20)

$$\frac{\csc{\left(-10 + \frac{\pi}{2} \right)}}{2 \csc{\left(20 \right)}}$$

                        tan(10)                        
-------------------------------------------------------
                                            2          
/       2    \ /       2   \ /       2     \     4     
\1 + tan (10)/*\1 - tan (5)/*\1 - tan (5/2)/ *cos (5/2)

$$\frac{\tan{\left(10 \right)}}{\left(1 - \tan^{2}{\left(\frac{5}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right) \cos^{4}{\left(\frac{5}{2} \right)}}$$

     2                      
  sec (5)*sec(10)*sin(10)   
----------------------------
/       2    \ /       2   \
\1 + tan (10)/*\1 - tan (5)/

$$\frac{\sin{\left(10 \right)} \sec^{2}{\left(5 \right)} \sec{\left(10 \right)}}{\left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right)}$$

                                  2                   
                   /       2     \                    
                   \1 + cot (5/2)/                    
------------------------------------------------------
                                             2        
/       1    \ /       1   \ /        2     \         
|1 + --------|*|1 - -------|*\-1 + cot (5/2)/ *cot(10)
|       2    | |       2   |                          
\    cot (10)/ \    cot (5)/

$$\frac{\left(1 + \cot^{2}{\left(\frac{5}{2} \right)}\right)^{2}}{\left(-1 + \cot^{2}{\left(\frac{5}{2} \right)}\right)^{2} \left(1 - \frac{1}{\cot^{2}{\left(5 \right)}}\right) \left(\frac{1}{\cot^{2}{\left(10 \right)}} + 1\right) \cot{\left(10 \right)}}$$

                          2                  
           /       2     \                   
           \1 + tan (5/2)/ *tan(10)          
---------------------------------------------
                                            2
/       2    \ /       2   \ /       2     \ 
\1 + tan (10)/*\1 - tan (5)/*\1 - tan (5/2)/

$$\frac{\left(\tan^{2}{\left(\frac{5}{2} \right)} + 1\right)^{2} \tan{\left(10 \right)}}{\left(1 - \tan^{2}{\left(\frac{5}{2} \right)}\right)^{2} \left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right)}$$

  2*cot(5) 
-----------
       2   
1 + cot (5)

$$\frac{2 \cot{\left(5 \right)}}{\cot^{2}{\left(5 \right)} + 1}$$

   sec(10)    
--------------
     /     pi\
2*sec|20 - --|
     \     2 /

$$\frac{\sec{\left(10 \right)}}{2 \sec{\left(20 - \frac{\pi}{2} \right)}}$$

   /       2   \            
   \1 + tan (5)/*tan(10)    
----------------------------
/       2    \ /       2   \
\1 + tan (10)/*\1 - tan (5)/

$$\frac{\left(1 + \tan^{2}{\left(5 \right)}\right) \tan{\left(10 \right)}}{\left(1 - \tan^{2}{\left(5 \right)}\right) \left(\tan^{2}{\left(10 \right)} + 1\right)}$$

(1 + tan(5)^2)*tan(10)/((1 + tan(10)^2)*(1 - tan(5)^2))

Respuesta numérica [src]

-0.544021110889370

-0.544021110889370

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

¿Cómo vas a descomponer esta sin20/(2*cos10) expresión en fracciones?

Solución