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Simplificación de expresiones/ Descomposición en fracciones simples/ (sin10)/(2*cos5)

¿Cómo vas a descomponer esta (sin10)/(2*cos5) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(10) 
--------
2*cos(5)
$$\frac{\sin{\left(10 \right)}}{2 \cos{\left(5 \right)}}$$ 
sin(10)/((2*cos(5)))
Simplificación general [src] 
sin(5)
$$\sin{\left(5 \right)}$$ 
sin(5)
Potencias [src] 
   /   -10*I    10*I\ 
-I*\- e      + e    / 
----------------------
     / -5*I    5*I\   
   2*\e     + e   /
$$- \frac{i \left(e^{10 i} - e^{- 10 i}\right)}{2 \left(e^{5 i} + e^{- 5 i}\right)}$$ 
-i*(-exp(-10*i) + exp(10*i))/(2*(exp(-5*i) + exp(5*i)))
Abrimos la expresión [src] 
                  7                                     3                                                                              9                                      5                   
           512*sin (1)*cos(1)                     80*sin (1)*cos(1)                       5*cos(1)*sin(1)                       256*sin (1)*cos(1)                     336*sin (1)*cos(1)         
- ------------------------------------ - ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------
          3                       5              3                       5              3                       5              3                       5              3                       5   
  - 20*cos (1) + 5*cos(1) + 16*cos (1)   - 20*cos (1) + 5*cos(1) + 16*cos (1)   - 20*cos (1) + 5*cos(1) + 16*cos (1)   - 20*cos (1) + 5*cos(1) + 16*cos (1)   - 20*cos (1) + 5*cos(1) + 16*cos (1)
$$- \frac{512 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{- 20 \cos^{3}{\left(1 \right)} + 16 \cos^{5}{\left(1 \right)} + 5 \cos{\left(1 \right)}} - \frac{80 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{- 20 \cos^{3}{\left(1 \right)} + 16 \cos^{5}{\left(1 \right)} + 5 \cos{\left(1 \right)}} + \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{- 20 \cos^{3}{\left(1 \right)} + 16 \cos^{5}{\left(1 \right)} + 5 \cos{\left(1 \right)}} + \frac{256 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{- 20 \cos^{3}{\left(1 \right)} + 16 \cos^{5}{\left(1 \right)} + 5 \cos{\left(1 \right)}} + \frac{336 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{- 20 \cos^{3}{\left(1 \right)} + 16 \cos^{5}{\left(1 \right)} + 5 \cos{\left(1 \right)}}$$ 
-512*sin(1)^7*cos(1)/(-20*cos(1)^3 + 5*cos(1) + 16*cos(1)^5) - 80*sin(1)^3*cos(1)/(-20*cos(1)^3 + 5*cos(1) + 16*cos(1)^5) + 5*cos(1)*sin(1)/(-20*cos(1)^3 + 5*cos(1) + 16*cos(1)^5) + 256*sin(1)^9*cos(1)/(-20*cos(1)^3 + 5*cos(1) + 16*cos(1)^5) + 336*sin(1)^5*cos(1)/(-20*cos(1)^3 + 5*cos(1) + 16*cos(1)^5)
Parte trigonométrica [src] 
  2*tan(5/2) 
-------------
       2     
1 + tan (5/2)
$$\frac{2 \tan{\left(\frac{5}{2} \right)}}{\tan^{2}{\left(\frac{5}{2} \right)} + 1}$$ 
    sec(5)    
--------------
     /     pi\
2*sec|10 - --|
     \     2 /
$$\frac{\sec{\left(5 \right)}}{2 \sec{\left(10 - \frac{\pi}{2} \right)}}$$ 
   /     pi\
csc|-5 + --|
   \     2 /
------------
 2*csc(10)
$$\frac{\csc{\left(-5 + \frac{\pi}{2} \right)}}{2 \csc{\left(10 \right)}}$$ 
   /    pi\
cos|5 - --|
   \    2 /
$$\cos{\left(5 - \frac{\pi}{2} \right)}$$ 
    /       2     \          
    \1 + tan (5/2)/*tan(5)   
-----------------------------
/       2   \ /       2     \
\1 + tan (5)/*\1 - tan (5/2)/
$$\frac{\left(\tan^{2}{\left(\frac{5}{2} \right)} + 1\right) \tan{\left(5 \right)}}{\left(1 - \tan^{2}{\left(\frac{5}{2} \right)}\right) \left(1 + \tan^{2}{\left(5 \right)}\right)}$$ 
  sec(5) 
---------
2*csc(10)
$$\frac{\sec{\left(5 \right)}}{2 \csc{\left(10 \right)}}$$ 
  1   
------
csc(5)
$$\frac{1}{\csc{\left(5 \right)}}$$ 
sin(5)
$$\sin{\left(5 \right)}$$ 
   sin(10)   
-------------
     /    pi\
2*sin|5 + --|
     \    2 /
$$\frac{\sin{\left(10 \right)}}{2 \sin{\left(\frac{\pi}{2} + 5 \right)}}$$ 
    /       2     \           
    \1 + cot (5/2)/*cot(5)    
------------------------------
/       2   \ /        2     \
\1 + cot (5)/*\-1 + cot (5/2)/
$$\frac{\left(1 + \cot^{2}{\left(\frac{5}{2} \right)}\right) \cot{\left(5 \right)}}{\left(-1 + \cot^{2}{\left(\frac{5}{2} \right)}\right) \left(\cot^{2}{\left(5 \right)} + 1\right)}$$ 
     1     
-----------
   /    pi\
sec|5 - --|
   \    2 /
$$\frac{1}{\sec{\left(5 - \frac{\pi}{2} \right)}}$$ 
   /     pi\
cos|10 - --|
   \     2 /
------------
  2*cos(5)
$$\frac{\cos{\left(10 - \frac{\pi}{2} \right)}}{2 \cos{\left(5 \right)}}$$ 
  2*cot(5/2) 
-------------
       2     
1 + cot (5/2)
$$\frac{2 \cot{\left(\frac{5}{2} \right)}}{1 + \cot^{2}{\left(\frac{5}{2} \right)}}$$ 
2*cot(5/2)/(1 + cot(5/2)^2)
Respuesta numérica [src] 
-0.958924274663138
-0.958924274663138
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