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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
 sin(20) 
---------
2*cos(10)
sin⁡(20)2cos⁡(10)\frac{\sin{\left(20 \right)}}{2 \cos{\left(10 \right)}} 
sin(20)/((2*cos(10)))
Simplificación general [src] 
sin(10)
sin⁡(10)\sin{\left(10 \right)} 
sin(10)
Potencias [src] 
   /   -20*I    20*I\ 
-I*\- e      + e    / 
----------------------
    / -10*I    10*I\  
  2*\e      + e    /
−i(−e−20i+e20i)2(e10i+e−10i)- \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)
2293760sin⁡13(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)+512512sin⁡9(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)+1179648sin⁡17(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)+12672sin⁡5(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)+10sin⁡(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)−660sin⁡3(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)−262144sin⁡19(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)−109824sin⁡7(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)−2228224sin⁡15(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(1)−1397760sin⁡11(1)cos⁡(1)−400cos⁡4(1)−1280cos⁡8(1)−1+512cos⁡10(1)+50cos⁡2(1)+1120cos⁡6(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 /
1sec⁡(10−π2)\frac{1}{\sec{\left(10 - \frac{\pi}{2} \right)}} 
              tan(10)               
------------------------------------
/       2    \ /       2   \    2   
\1 + tan (10)/*\1 - tan (5)/*cos (5)
tan⁡(10)(1−tan⁡2(5))(tan⁡2(10)+1)cos⁡2(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 /
sin⁡(20)2sin⁡(π2+10)\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)/
(cot⁡2(5)+1)cot⁡(10)(−1+cot⁡2(5))(1+cot⁡2(10))\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)
sec⁡(10)2csc⁡(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) /
2sin⁡2(10)(−4sin⁡4(5)sin⁡2(10)+1)(4sin⁡4(10)sin⁡2(20)+1)sin⁡(20)sin⁡2(π2+5)\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)
cos⁡(20−π2)2cos⁡(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 //
sec⁡2(5)sec⁡(10)(−sec⁡2(5)sec⁡2(5−π2)+1)(sec⁡2(10)sec⁡2(10−π2)+1)sec⁡(10−π2)\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)
1csc⁡(10)\frac{1}{\csc{\left(10 \right)}} 
   /     pi\
cos|10 - --|
   \     2 /
cos⁡(10−π2)\cos{\left(10 - \frac{\pi}{2} \right)} 
sin(10)
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)   /
csc⁡(−10+π2)csc⁡2(−5+π2)(−csc⁡2(−5+π2)csc⁡2(5)+1)(csc⁡2(−10+π2)csc⁡2(10)+1)csc⁡(10)\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)
tan⁡(10)(−1+cot⁡2(52))2(1−tan⁡2(5))(tan⁡2(10)+1)sin⁡4(52)\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)
2tan⁡(5)1+tan⁡2(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)
sin⁡(10)(1−tan⁡2(5))(tan⁡2(10)+1)cos⁡2(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)   /
cos⁡(10−π2)(−cos⁡2(5−π2)cos⁡2(5)+1)(cos⁡2(10−π2)cos⁡2(10)+1)cos⁡2(5)cos⁡(10)\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) /
2sin⁡2(10)(−4sin⁡4(5)sin⁡2(10)+1)(4sin⁡4(10)sin⁡2(20)+1)sin⁡(20)cos⁡2(5)\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)} \cos^{2}{\left(5 \right)}} 
   /      pi\
csc|-10 + --|
   \      2 /
-------------
  2*csc(20)
csc⁡(−10+π2)2csc⁡(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)
tan⁡(10)(1−tan⁡2(52))2(1−tan⁡2(5))(tan⁡2(10)+1)cos⁡4(52)\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)/
sin⁡(10)sec⁡2(5)sec⁡(10)(1−tan⁡2(5))(tan⁡2(10)+1)\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)/
(1+cot⁡2(52))2(−1+cot⁡2(52))2(1−1cot⁡2(5))(1cot⁡2(10)+1)cot⁡(10)\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)/
(tan⁡2(52)+1)2tan⁡(10)(1−tan⁡2(52))2(1−tan⁡2(5))(tan⁡2(10)+1)\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)
2cot⁡(5)cot⁡2(5)+1\frac{2 \cot{\left(5 \right)}}{\cot^{2}{\left(5 \right)} + 1} 
   sec(10)    
--------------
     /     pi\
2*sec|20 - --|
     \     2 /
sec⁡(10)2sec⁡(20−π2)\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)/
(1+tan⁡2(5))tan⁡(10)(1−tan⁡2(5))(tan⁡2(10)+1)\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
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