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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⁡(73(n4+2))\tan{\left(\frac{7}{\sqrt{3 \left(n^{4} + 2\right)}} \right)} 
tan(7/sqrt(3*(n^4 + 2)))
Simplificación general [src] 
   /       ___   \
   |   7*\/ 3    |
tan|-------------|
   |     ________|
   |    /      4 |
   \3*\/  2 + n  /
tan⁡(733n4+2)\tan{\left(\frac{7 \sqrt{3}}{3 \sqrt{n^{4} + 2}} \right)} 
tan(7*sqrt(3)/(3*sqrt(2 + n^4)))
Descomposición de una fracción [src] 
tan(7/sqrt(6 + 3*n^4))
tan⁡(73n4+6)\tan{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)} 
   /      7      \
tan|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
Respuesta numérica [src] 
tan(7/sqrt(3*(n^4 + 2)))
tan(7/sqrt(3*(n^4 + 2)))
Potencias [src] 
   /      7      \
tan|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
tan⁡(73n4+6)\tan{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)} 
  /        7*I              -7*I    \
  |   -------------    -------------|
  |      __________       __________|
  |     /        4       /        4 |
  |   \/  6 + 3*n      \/  6 + 3*n  |
I*\- e              + e             /
-------------------------------------
         -7*I             7*I        
    -------------    -------------   
       __________       __________   
      /        4       /        4    
    \/  6 + 3*n      \/  6 + 3*n     
   e              + e
i(−e7i3n4+6+e−7i3n4+6)e7i3n4+6+e−7i3n4+6\frac{i \left(- e^{\frac{7 i}{\sqrt{3 n^{4} + 6}}} + e^{- \frac{7 i}{\sqrt{3 n^{4} + 6}}}\right)}{e^{\frac{7 i}{\sqrt{3 n^{4} + 6}}} + e^{- \frac{7 i}{\sqrt{3 n^{4} + 6}}}} 
i*(-exp(7*i/sqrt(6 + 3*n^4)) + exp(-7*i/sqrt(6 + 3*n^4)))/(exp(-7*i/sqrt(6 + 3*n^4)) + exp(7*i/sqrt(6 + 3*n^4)))
Combinatoria [src] 
   /      7      \
tan|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
tan⁡(73n4+6)\tan{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)} 
tan(7/sqrt(6 + 3*n^4))
Unión de expresiones racionales [src] 
   /      7      \
tan|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
tan⁡(73n4+6)\tan{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)} 
tan(7/sqrt(6 + 3*n^4))
Denominador común [src] 
   /       ___   \
   |   7*\/ 3    |
tan|-------------|
   |     ________|
   |    /      4 |
   \3*\/  2 + n  /
tan⁡(733n4+2)\tan{\left(\frac{7 \sqrt{3}}{3 \sqrt{n^{4} + 2}} \right)} 
tan(7*sqrt(3)/(3*sqrt(2 + n^4)))
Denominador racional [src] 
   /       ___   \
   |   7*\/ 3    |
tan|-------------|
   |     ________|
   |    /      4 |
   \3*\/  2 + n  /
tan⁡(733n4+2)\tan{\left(\frac{7 \sqrt{3}}{3 \sqrt{n^{4} + 2}} \right)} 
tan(7*sqrt(3)/(3*sqrt(2 + n^4)))
Abrimos la expresión [src] 
                                 7/      1      \                                                                3/      1      \                                                              /      1      \                                                               5/      1      \                          
                              tan |-------------|                                                          35*tan |-------------|                                                         7*tan|-------------|                                                         21*tan |-------------|                          
                                  |   __________|                                                                 |   __________|                                                              |   __________|                                                                |   __________|                          
                                  |  /        4 |                                                                 |  /        4 |                                                              |  /        4 |                                                                |  /        4 |                          
                                  \\/  6 + 3*n  /                                                                 \\/  6 + 3*n  /                                                              \\/  6 + 3*n  /                                                                \\/  6 + 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 |
             \\/  6 + 3*n  /         \\/  6 + 3*n  /          \\/  6 + 3*n  /              \\/  6 + 3*n  /         \\/  6 + 3*n  /          \\/  6 + 3*n  /              \\/  6 + 3*n  /         \\/  6 + 3*n  /          \\/  6 + 3*n  /              \\/  6 + 3*n  /         \\/  6 + 3*n  /          \\/  6 + 3*n  /
−tan⁡7(13n4+6)−7tan⁡6(13n4+6)+35tan⁡4(13n4+6)−21tan⁡2(13n4+6)+1+21tan⁡5(13n4+6)−7tan⁡6(13n4+6)+35tan⁡4(13n4+6)−21tan⁡2(13n4+6)+1−35tan⁡3(13n4+6)−7tan⁡6(13n4+6)+35tan⁡4(13n4+6)−21tan⁡2(13n4+6)+1+7tan⁡(13n4+6)−7tan⁡6(13n4+6)+35tan⁡4(13n4+6)−21tan⁡2(13n4+6)+1- \frac{\tan^{7}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 1} + \frac{21 \tan^{5}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 1} - \frac{35 \tan^{3}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 1} + \frac{7 \tan{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)}}{- 7 \tan^{6}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 35 \tan^{4}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} - 21 \tan^{2}{\left(\frac{1}{\sqrt{3 n^{4} + 6}} \right)} + 1} 
   /       ___   \
   |   7*\/ 3    |
tan|-------------|
   |     ________|
   |    /  4     |
   \3*\/  n  + 2 /
tan⁡(733n4+2)\tan{\left(\frac{7 \sqrt{3}}{3 \sqrt{n^{4} + 2}} \right)} 
tan(7*sqrt(3)/(3*sqrt(n^4 + 2)))
Parte trigonométrica [src] 
        1         
------------------
   /      7      \
cot|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
1cot⁡(73n4+6)\frac{1}{\cot{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}} 
     2/      7      \
2*sin |-------------|
      |   __________|
      |  /        4 |
      \\/  6 + 3*n  /
---------------------
     /      14     \ 
  sin|-------------| 
     |   __________| 
     |  /        4 | 
     \\/  6 + 3*n  /
2sin⁡2(73n4+6)sin⁡(143n4+6)\frac{2 \sin^{2}{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}}{\sin{\left(\frac{14}{\sqrt{3 n^{4} + 6}} \right)}} 
   /      7      \
tan|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
tan⁡(73n4+6)\tan{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)} 
   /pi         7      \
csc|-- - -------------|
   |2       __________|
   |       /        4 |
   \     \/  6 + 3*n  /
-----------------------
      /      7      \  
   csc|-------------|  
      |   __________|  
      |  /        4 |  
      \\/  6 + 3*n  /
csc⁡(π2−73n4+6)csc⁡(73n4+6)\frac{\csc{\left(\frac{\pi}{2} - \frac{7}{\sqrt{3 n^{4} + 6}} \right)}}{\csc{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}} 
   /      7      \
sin|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
------------------
   /      7      \
cos|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
sin⁡(73n4+6)cos⁡(73n4+6)\frac{\sin{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}}{\cos{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}} 
   /      7      \
sec|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
------------------
   /      7      \
csc|-------------|
   |   __________|
   |  /        4 |
   \\/  6 + 3*n  /
sec⁡(73n4+6)csc⁡(73n4+6)\frac{\sec{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}}{\csc{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}} 
   /      7         pi\
cos|------------- - --|
   |   __________   2 |
   |  /        4      |
   \\/  6 + 3*n       /
-----------------------
      /      7      \  
   cos|-------------|  
      |   __________|  
      |  /        4 |  
      \\/  6 + 3*n  /
cos⁡(−π2+73n4+6)cos⁡(73n4+6)\frac{\cos{\left(- \frac{\pi}{2} + \frac{7}{\sqrt{3 n^{4} + 6}} \right)}}{\cos{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}} 
      /      7      \  
   sec|-------------|  
      |   __________|  
      |  /        4 |  
      \\/  6 + 3*n  /  
-----------------------
   /      7         pi\
sec|------------- - --|
   |   __________   2 |
   |  /        4      |
   \\/  6 + 3*n       /
sec⁡(73n4+6)sec⁡(−π2+73n4+6)\frac{\sec{\left(\frac{7}{\sqrt{3 n^{4} + 6}} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{7}{\sqrt{3 n^{4} + 6}} \right)}} 
sec(7/sqrt(6 + 3*n^4))/sec(7/sqrt(6 + 3*n^4) - pi/2)
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