Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sin2x/(28(cos^2x-sin^2x))

¿Cómo vas a descomponer esta sin2x/(28(cos^2x-sin^2x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
       sin(2*x)       
----------------------
   /   2         2   \
28*\cos (x) - sin (x)/
sin⁡(2x)28(−sin⁡2(x)+cos⁡2(x))\frac{\sin{\left(2 x \right)}}{28 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)} 
sin(2*x)/((28*(cos(x)^2 - sin(x)^2)))
Simplificación general [src] 
tan(2*x)
--------
   28
tan⁡(2x)28\frac{\tan{\left(2 x \right)}}{28} 
tan(2*x)/28
Respuesta numérica [src] 
sin(2*x)/(28.0*cos(x)^2 - 28.0*sin(x)^2)
sin(2*x)/(28.0*cos(x)^2 - 28.0*sin(x)^2)
Denominador racional [src] 
         sin(2*x)        
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
sin⁡(2x)−28sin⁡2(x)+28cos⁡2(x)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Combinatoria [src] 
                sin(2*x)               
---------------------------------------
28*(-sin(x) + cos(x))*(cos(x) + sin(x))
sin⁡(2x)28(−sin⁡(x)+cos⁡(x))(sin⁡(x)+cos⁡(x))\frac{\sin{\left(2 x \right)}}{28 \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)} 
sin(2*x)/(28*(-sin(x) + cos(x))*(cos(x) + sin(x)))
Unión de expresiones racionales [src] 
         sin(2*x)        
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
sin⁡(2x)−28sin⁡2(x)+28cos⁡2(x)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Denominador común [src] 
         sin(2*x)        
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
sin⁡(2x)−28sin⁡2(x)+28cos⁡2(x)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Compilar la expresión [src] 
         sin(2*x)        
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
sin⁡(2x)−28sin⁡2(x)+28cos⁡2(x)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Potencias [src] 
         sin(2*x)        
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
sin⁡(2x)−28sin⁡2(x)+28cos⁡2(x)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
             /   -2*I*x    2*I*x\           
          -I*\- e       + e     /           
--------------------------------------------
  /                                       2\
  |                  2      / I*x    -I*x\ |
  |  /   -I*x    I*x\       |e      e    | |
2*|7*\- e     + e   /  + 28*|---- + -----| |
  \                         \ 2       2  / /
−i(e2ix−e−2ix)2(28(eix2+e−ix2)2+7(eix−e−ix)2)- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(28 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2} + 7 \left(e^{i x} - e^{- i x}\right)^{2}\right)} 
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(7*(-exp(-i*x) + exp(i*x))^2 + 28*(exp(i*x)/2 + exp(-i*x)/2)^2))
Parte trigonométrica [src] 
           sin(2*x)           
------------------------------
        2            2/    pi\
- 28*sin (x) + 28*sin |x + --|
                      \    2 /
sin⁡(2x)−28sin⁡2(x)+28sin⁡2(x+π2)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \sin^{2}{\left(x + \frac{\pi}{2} \right)}} 
         sin(2*x)        
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
sin⁡(2x)−28sin⁡2(x)+28cos⁡2(x)\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
                   1                    
----------------------------------------
/       28           28  \    /      pi\
|- ------------ + -------|*sec|2*x - --|
|     2/    pi\      2   |    \      2 /
|  sec |x - --|   sec (x)|              
\      \    2 /          /
1(−28sec⁡2(x−π2)+28sec⁡2(x))sec⁡(2x−π2)\frac{1}{\left(- \frac{28}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + \frac{28}{\sec^{2}{\left(x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} 
   /      pi\
cos|2*x - --|
   \      2 /
-------------
 28*cos(2*x)
cos⁡(2x−π2)28cos⁡(2x)\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{28 \cos{\left(2 x \right)}} 
              1               
------------------------------
/     28        28  \         
|- ------- + -------|*csc(2*x)
|     2         2   |         
\  csc (x)   sec (x)/
1(28sec⁡2(x)−28csc⁡2(x))csc⁡(2x)\frac{1}{\left(\frac{28}{\sec^{2}{\left(x \right)}} - \frac{28}{\csc^{2}{\left(x \right)}}\right) \csc{\left(2 x \right)}} 
     1     
-----------
28*cot(2*x)
128cot⁡(2x)\frac{1}{28 \cot{\left(2 x \right)}} 
tan(2*x)
--------
   28
tan⁡(2x)28\frac{\tan{\left(2 x \right)}}{28} 
                 1                 
-----------------------------------
/     28          28     \         
|- ------- + ------------|*csc(2*x)
|     2         2/pi    \|         
|  csc (x)   csc |-- - x||         
\                \2     //
1(28csc⁡2(−x+π2)−28csc⁡2(x))csc⁡(2x)\frac{1}{\left(\frac{28}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - \frac{28}{\csc^{2}{\left(x \right)}}\right) \csc{\left(2 x \right)}} 
    2      
 sin (2*x) 
-----------
14*sin(4*x)
sin⁡2(2x)14sin⁡(4x)\frac{\sin^{2}{\left(2 x \right)}}{14 \sin{\left(4 x \right)}} 
                      2*tan(x)                      
----------------------------------------------------
              /                                   2\
              |          2/x\        /       2/x\\ |
              |   112*tan |-|     28*|1 - tan |-|| |
/       2   \ |           \2/        \        \2// |
\1 + tan (x)/*|- -------------- + -----------------|
              |               2                  2 |
              |  /       2/x\\      /       2/x\\  |
              |  |1 + tan |-||      |1 + tan |-||  |
              \  \        \2//      \        \2//  /
2tan⁡(x)(28(1−tan⁡2(x2))2(tan⁡2(x2)+1)2−112tan⁡2(x2)(tan⁡2(x2)+1)2)(tan⁡2(x)+1)\frac{2 \tan{\left(x \right)}}{\left(\frac{28 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - \frac{112 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
    sec(2*x)    
----------------
      /      pi\
28*sec|2*x - --|
      \      2 /
sec⁡(2x)28sec⁡(2x−π2)\frac{\sec{\left(2 x \right)}}{28 \sec{\left(2 x - \frac{\pi}{2} \right)}} 
           /      pi\         
        cos|2*x - --|         
           \      2 /         
------------------------------
        2/    pi\         2   
- 28*cos |x - --| + 28*cos (x)
         \    2 /
cos⁡(2x−π2)28cos⁡2(x)−28cos⁡2(x−π2)\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{28 \cos^{2}{\left(x \right)} - 28 \cos^{2}{\left(x - \frac{\pi}{2} \right)}} 
                       2*cot(x)                      
-----------------------------------------------------
              /                                    2\
              |          2/x\        /        2/x\\ |
              |   112*cot |-|     28*|-1 + cot |-|| |
/       2   \ |           \2/        \         \2// |
\1 + cot (x)/*|- -------------- + ------------------|
              |               2                  2  |
              |  /       2/x\\      /       2/x\\   |
              |  |1 + cot |-||      |1 + cot |-||   |
              \  \        \2//      \        \2//   /
2cot⁡(x)(28(cot⁡2(x2)−1)2(cot⁡2(x2)+1)2−112cot⁡2(x2)(cot⁡2(x2)+1)2)(cot⁡2(x)+1)\frac{2 \cot{\left(x \right)}}{\left(\frac{28 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - \frac{112 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
   /pi      \
csc|-- - 2*x|
   \2       /
-------------
 28*csc(2*x)
csc⁡(−2x+π2)28csc⁡(2x)\frac{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}{28 \csc{\left(2 x \right)}} 
csc(pi/2 - 2*x)/(28*csc(2*x))
Abrimos la expresión [src] 
     2*cos(x)*sin(x)     
-------------------------
        2            2   
- 28*sin (x) + 28*cos (x)
2sin⁡(x)cos⁡(x)−28sin⁡2(x)+28cos⁡2(x)\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}} 
2*cos(x)*sin(x)/(-28*sin(x)^2 + 28*cos(x)^2)
    © Sr Examen – Калькулятор