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Simplificación de expresiones/ Descomposición en fracciones simples/ tg(7/(sqrt(3)(n^4+2)))

¿Cómo vas a descomponer esta tg(7/(sqrt(3)(n^4+2))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /      7       \
tan|--------------|
   |  ___ / 4    \|
   \\/ 3 *\n  + 2//
$$\tan{\left(\frac{7}{\sqrt{3} \left(n^{4} + 2\right)} \right)}$$ 
tan(7/((sqrt(3)*(n^4 + 2))))
Descomposición de una fracción [src] 
tan(7/(2*sqrt(3) + sqrt(3)*n^4))
$$\tan{\left(\frac{7}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)}$$ 
   /        7         \
tan|------------------|
   |    ___     ___  4|
   \2*\/ 3  + \/ 3 *n /
Simplificación general [src] 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
tan(7*sqrt(3)/(3*(2 + n^4)))
Denominador racional [src] 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
tan(7*sqrt(3)/(3*(2 + n^4)))
Combinatoria [src] 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
tan(7*sqrt(3)/(3*(2 + n^4)))
Denominador común [src] 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
tan(7*sqrt(3)/(3*(2 + n^4)))
Abrimos la expresión [src] 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  / 4    \|
   \3*\n  + 2//
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
                                      7/        1         \                                                                         3/        1         \                                                                        /        1         \                                                                         5/        1         \                                
                                   tan |------------------|                                                                   35*tan |------------------|                                                                   7*tan|------------------|                                                                   21*tan |------------------|                                
                                       |    ___     ___  4|                                                                          |    ___     ___  4|                                                                        |    ___     ___  4|                                                                          |    ___     ___  4|                                
                                       \2*\/ 3  + \/ 3 *n /                                                                          \2*\/ 3  + \/ 3 *n /                                                                        \2*\/ 3  + \/ 3 *n /                                                                          \2*\/ 3  + \/ 3 *n /                                
- ------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------
            2/        1         \        6/        1         \         4/        1         \             2/        1         \        6/        1         \         4/        1         \             2/        1         \        6/        1         \         4/        1         \             2/        1         \        6/        1         \         4/        1         \
  1 - 21*tan |------------------| - 7*tan |------------------| + 35*tan |------------------|   1 - 21*tan |------------------| - 7*tan |------------------| + 35*tan |------------------|   1 - 21*tan |------------------| - 7*tan |------------------| + 35*tan |------------------|   1 - 21*tan |------------------| - 7*tan |------------------| + 35*tan |------------------|
             |    ___     ___  4|         |    ___     ___  4|          |    ___     ___  4|              |    ___     ___  4|         |    ___     ___  4|          |    ___     ___  4|              |    ___     ___  4|         |    ___     ___  4|          |    ___     ___  4|              |    ___     ___  4|         |    ___     ___  4|          |    ___     ___  4|
             \2*\/ 3  + \/ 3 *n /         \2*\/ 3  + \/ 3 *n /          \2*\/ 3  + \/ 3 *n /              \2*\/ 3  + \/ 3 *n /         \2*\/ 3  + \/ 3 *n /          \2*\/ 3  + \/ 3 *n /              \2*\/ 3  + \/ 3 *n /         \2*\/ 3  + \/ 3 *n /          \2*\/ 3  + \/ 3 *n /              \2*\/ 3  + \/ 3 *n /         \2*\/ 3  + \/ 3 *n /          \2*\/ 3  + \/ 3 *n /
$$- \frac{\tan^{7}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 1} + \frac{21 \tan^{5}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 1} - \frac{35 \tan^{3}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 1} + \frac{7 \tan{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3} n^{4} + 2 \sqrt{3}} \right)} + 1}$$ 
-tan(1/(2*sqrt(3) + sqrt(3)*n^4))^7/(1 - 21*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^2 - 7*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^6 + 35*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^4) - 35*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^3/(1 - 21*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^2 - 7*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^6 + 35*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^4) + 7*tan(1/(2*sqrt(3) + sqrt(3)*n^4))/(1 - 21*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^2 - 7*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^6 + 35*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^4) + 21*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^5/(1 - 21*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^2 - 7*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^6 + 35*tan(1/(2*sqrt(3) + sqrt(3)*n^4))^4)
Parte trigonométrica [src] 
       1       
---------------
   /     ___  \
   | 7*\/ 3   |
cot|----------|
   |  /     4\|
   \3*\2 + n //
$$\frac{1}{\cot{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
      /     ___  \
     2| 7*\/ 3   |
2*sin |----------|
      |  /     4\|
      \3*\2 + n //
------------------
    /      ___ \  
    | 14*\/ 3  |  
 sin|----------|  
    |  /     4\|  
    \3*\2 + n //
$$\frac{2 \sin^{2}{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}{\sin{\left(\frac{14 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
   /     ___  \
   | 7*\/ 3   |
sec|----------|
   |  /     4\|
   \3*\2 + n //
---------------
   /     ___  \
   | 7*\/ 3   |
csc|----------|
   |  /     4\|
   \3*\2 + n //
$$\frac{\sec{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}{\csc{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
   /            ___  \
   |  pi    7*\/ 3   |
cos|- -- + ----------|
   |  2      /     4\|
   \       3*\2 + n //
----------------------
      /     ___  \    
      | 7*\/ 3   |    
   cos|----------|    
      |  /     4\|    
      \3*\2 + n //
$$\frac{\cos{\left(- \frac{\pi}{2} + \frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}{\cos{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
      /     ___  \    
      | 7*\/ 3   |    
   sec|----------|    
      |  /     4\|    
      \3*\2 + n //    
----------------------
   /            ___  \
   |  pi    7*\/ 3   |
sec|- -- + ----------|
   |  2      /     4\|
   \       3*\2 + n //
$$\frac{\sec{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
   /     ___  \
   | 7*\/ 3   |
sin|----------|
   |  /     4\|
   \3*\2 + n //
---------------
   /     ___  \
   | 7*\/ 3   |
cos|----------|
   |  /     4\|
   \3*\2 + n //
$$\frac{\sin{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}{\cos{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
   /          ___  \
   |pi    7*\/ 3   |
csc|-- - ----------|
   |2      /     4\|
   \     3*\2 + n //
--------------------
     /     ___  \   
     | 7*\/ 3   |   
  csc|----------|   
     |  /     4\|   
     \3*\2 + n //
$$\frac{\csc{\left(\frac{\pi}{2} - \frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}{\csc{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}}$$ 
csc(pi/2 - 7*sqrt(3)/(3*(2 + n^4)))/csc(7*sqrt(3)/(3*(2 + n^4)))
Respuesta numérica [src] 
tan(7/((sqrt(3)*(n^4 + 2))))
tan(7/((sqrt(3)*(n^4 + 2))))
Potencias [src] 
  /         ___            ___\
  |   7*I*\/ 3      -7*I*\/ 3 |
  |   ----------    ----------|
  |     /     4\      /     4\|
  |   3*\2 + n /    3*\2 + n /|
I*\- e           + e          /
-------------------------------
           ___          ___    
    -7*I*\/ 3     7*I*\/ 3     
    ----------    ----------   
      /     4\      /     4\   
    3*\2 + n /    3*\2 + n /   
   e           + e
$$\frac{i \left(- e^{\frac{7 \sqrt{3} i}{3 \left(n^{4} + 2\right)}} + e^{- \frac{7 \sqrt{3} i}{3 \left(n^{4} + 2\right)}}\right)}{e^{\frac{7 \sqrt{3} i}{3 \left(n^{4} + 2\right)}} + e^{- \frac{7 \sqrt{3} i}{3 \left(n^{4} + 2\right)}}}$$ 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
tan(7*sqrt(3)/(3*(2 + n^4)))
Unión de expresiones racionales [src] 
   /     ___  \
   | 7*\/ 3   |
tan|----------|
   |  /     4\|
   \3*\2 + n //
$$\tan{\left(\frac{7 \sqrt{3}}{3 \left(n^{4} + 2\right)} \right)}$$ 
tan(7*sqrt(3)/(3*(2 + n^4)))
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