Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*x)/(2*sin(x)-cos(x))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
     sin(2*x)    
-----------------
2*sin(x) - cos(x)
sin⁡(2x)2sin⁡(x)−cos⁡(x)\frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} - \cos{\left(x \right)}} 
sin(2*x)/(2*sin(x) - cos(x))
Respuesta numérica [src] 
sin(2*x)/(-cos(x) + 2.0*sin(x))
sin(2*x)/(-cos(x) + 2.0*sin(x))
Combinatoria [src] 
    -sin(2*x)     
------------------
-2*sin(x) + cos(x)
−sin⁡(2x)−2sin⁡(x)+cos⁡(x)- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \cos{\left(x \right)}} 
-sin(2*x)/(-2*sin(x) + cos(x))
Denominador común [src] 
    -sin(2*x)     
------------------
-2*sin(x) + cos(x)
−sin⁡(2x)−2sin⁡(x)+cos⁡(x)- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \cos{\left(x \right)}} 
-sin(2*x)/(-2*sin(x) + cos(x))
Potencias [src] 
           /   -2*I*x    2*I*x\        
        -I*\- e       + e     /        
---------------------------------------
  /   I*x    -I*x                     \
  |  e      e         /   -I*x    I*x\|
2*|- ---- - ----- - I*\- e     + e   /|
  \   2       2                       /
−i(e2ix−e−2ix)2(−i(eix−e−ix)−eix2−e−ix2)- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(- i \left(e^{i x} - e^{- i x}\right) - \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)} 
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(-exp(i*x)/2 - exp(-i*x)/2 - i*(-exp(-i*x) + exp(i*x))))
Abrimos la expresión [src] 
 2*cos(x)*sin(x) 
-----------------
2*sin(x) - cos(x)
2sin⁡(x)cos⁡(x)2sin⁡(x)−cos⁡(x)\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{2 \sin{\left(x \right)} - \cos{\left(x \right)}} 
2*cos(x)*sin(x)/(2*sin(x) - cos(x))
Parte trigonométrica [src] 
                -1                  
------------------------------------
/  1           2     \    /      pi\
|------ - -----------|*sec|2*x - --|
|sec(x)      /    pi\|    \      2 /
|         sec|x - --||              
\            \    2 //
−1(−2sec⁡(x−π2)+1sec⁡(x))sec⁡(2x−π2)- \frac{1}{\left(- \frac{2}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} 
                  2*cot(x)                  
--------------------------------------------
              /          2/x\          /x\ \
              |  -1 + cot |-|     4*cot|-| |
/       2   \ |           \2/          \2/ |
\1 + cot (x)/*|- ------------ + -----------|
              |         2/x\           2/x\|
              |  1 + cot |-|    1 + cot |-||
              \          \2/            \2//
2cot⁡(x)(−cot⁡2(x2)−1cot⁡2(x2)+1+4cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(x)+1)\frac{2 \cot{\left(x \right)}}{\left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{4 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
        sin(2*x)        
------------------------
     /    pi\           
- sin|x + --| + 2*sin(x)
     \    2 /
sin⁡(2x)2sin⁡(x)−sin⁡(x+π2)\frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} - \sin{\left(x + \frac{\pi}{2} \right)}} 
                  1                   
--------------------------------------
/    1           2     \    /      pi\
|- ------ + -----------|*sec|2*x - --|
|  sec(x)      /    pi\|    \      2 /
|           sec|x - --||              
\              \    2 //
1(2sec⁡(x−π2)−1sec⁡(x))sec⁡(2x−π2)\frac{1}{\left(\frac{2}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} 
                1                
---------------------------------
/       1          2   \         
|- ----------- + ------|*csc(2*x)
|     /pi    \   csc(x)|         
|  csc|-- - x|         |         
\     \2     /         /
1(−1csc⁡(−x+π2)+2csc⁡(x))csc⁡(2x)\frac{1}{\left(- \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{2}{\csc{\left(x \right)}}\right) \csc{\left(2 x \right)}} 
        /      pi\     
     cos|2*x - --|     
        \      2 /     
-----------------------
               /    pi\
-cos(x) + 2*cos|x - --|
               \    2 /
cos⁡(2x−π2)−cos⁡(x)+2cos⁡(x−π2)\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{- \cos{\left(x \right)} + 2 \cos{\left(x - \frac{\pi}{2} \right)}} 
                  2*tan(x)                 
-------------------------------------------
              /         2/x\          /x\ \
              |  1 - tan |-|     4*tan|-| |
/       2   \ |          \2/          \2/ |
\1 + tan (x)/*|- ----------- + -----------|
              |         2/x\          2/x\|
              |  1 + tan |-|   1 + tan |-||
              \          \2/           \2//
2tan⁡(x)(−1−tan⁡2(x2)tan⁡2(x2)+1+4tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(x)+1)\frac{2 \tan{\left(x \right)}}{\left(- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{4 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
              -1               
-------------------------------
/     1          2   \         
|----------- - ------|*csc(2*x)
|   /pi    \   csc(x)|         
|csc|-- - x|         |         
\   \2     /         /
−1(1csc⁡(−x+π2)−2csc⁡(x))csc⁡(2x)- \frac{1}{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{2}{\csc{\left(x \right)}}\right) \csc{\left(2 x \right)}} 
        /      pi\      
    -cos|2*x - --|      
        \      2 /      
------------------------
       /    pi\         
- 2*cos|x - --| + cos(x)
       \    2 /
−cos⁡(2x−π2)cos⁡(x)−2cos⁡(x−π2)- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} - 2 \cos{\left(x - \frac{\pi}{2} \right)}} 
                -2*cot(x)                 
------------------------------------------
              /        2/x\          /x\ \
              |-1 + cot |-|     4*cot|-| |
/       2   \ |         \2/          \2/ |
\1 + cot (x)/*|------------ - -----------|
              |       2/x\           2/x\|
              |1 + cot |-|    1 + cot |-||
              \        \2/            \2//
−2cot⁡(x)(cot⁡2(x2)−1cot⁡2(x2)+1−4cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(x)+1)- \frac{2 \cot{\left(x \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
                -2*tan(x)                
-----------------------------------------
              /       2/x\          /x\ \
              |1 - tan |-|     4*tan|-| |
/       2   \ |        \2/          \2/ |
\1 + tan (x)/*|----------- - -----------|
              |       2/x\          2/x\|
              |1 + tan |-|   1 + tan |-||
              \        \2/           \2//
−2tan⁡(x)(1−tan⁡2(x2)tan⁡2(x2)+1−4tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(x)+1)- \frac{2 \tan{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
    -sin(2*x)     
------------------
-2*sin(x) + cos(x)
−sin⁡(2x)−2sin⁡(x)+cos⁡(x)- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \cos{\left(x \right)}} 
             1              
----------------------------
/    1        2   \         
|- ------ + ------|*csc(2*x)
\  sec(x)   csc(x)/
1(−1sec⁡(x)+2csc⁡(x))csc⁡(2x)\frac{1}{\left(- \frac{1}{\sec{\left(x \right)}} + \frac{2}{\csc{\left(x \right)}}\right) \csc{\left(2 x \right)}} 
       -sin(2*x)       
-----------------------
               /    pi\
-2*sin(x) + sin|x + --|
               \    2 /
−sin⁡(2x)−2sin⁡(x)+sin⁡(x+π2)- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}} 
-sin(2*x)/(-2*sin(x) + sin(x + pi/2))
    © Sr Examen – Калькулятор