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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x)/4-1/(sin(x)*4)-cos(x)/4

¿Cómo vas a descomponer esta sin(x)/4-1/(sin(x)*4)-cos(x)/4 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(x)      1       cos(x)
------ - -------- - ------
  4      sin(x)*4     4
(sin⁡(x)4−14sin⁡(x))−cos⁡(x)4\left(\frac{\sin{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}}\right) - \frac{\cos{\left(x \right)}}{4} 
sin(x)/4 - 1/(sin(x)*4) - cos(x)/4
Simplificación general [src] 
               ___    /    pi\
             \/ 2 *cos|x + --|
     1                \    4 /
- -------- - -----------------
  4*sin(x)           4
−2cos⁡(x+π4)4−14sin⁡(x)- \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
-1/(4*sin(x)) - sqrt(2)*cos(x + pi/4)/4
Respuesta numérica [src] 
0.25*sin(x) - 0.25/sin(x) - 0.25*cos(x)
0.25*sin(x) - 0.25/sin(x) - 0.25*cos(x)
Combinatoria [src] 
 /       2                   \ 
-\1 - sin (x) + cos(x)*sin(x)/ 
-------------------------------
            4*sin(x)
−−sin⁡2(x)+sin⁡(x)cos⁡(x)+14sin⁡(x)- \frac{- \sin^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} + 1}{4 \sin{\left(x \right)}} 
-(1 - sin(x)^2 + cos(x)*sin(x))/(4*sin(x))
Potencias [src] 
   I*x    -I*x                          /   -I*x    I*x\
  e      e               I            I*\- e     + e   /
- ---- - ----- - ------------------ - ------------------
   8       8       /   -I*x    I*x\           8         
                 2*\- e     + e   /
−i(eix−e−ix)8−eix8−e−ix8−i2(eix−e−ix)- \frac{i \left(e^{i x} - e^{- i x}\right)}{8} - \frac{e^{i x}}{8} - \frac{e^{- i x}}{8} - \frac{i}{2 \left(e^{i x} - e^{- i x}\right)} 
     1       cos(x)   sin(x)
- -------- - ------ + ------
  4*sin(x)     4        4
sin⁡(x)4−cos⁡(x)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
-1/(4*sin(x)) - cos(x)/4 + sin(x)/4
Denominador común [src] 
     1       cos(x)   sin(x)
- -------- - ------ + ------
  4*sin(x)     4        4
sin⁡(x)4−cos⁡(x)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
-1/(4*sin(x)) - cos(x)/4 + sin(x)/4
Denominador racional [src] 
            2                      
-16 + 16*sin (x) - 16*cos(x)*sin(x)
-----------------------------------
             64*sin(x)
16sin⁡2(x)−16sin⁡(x)cos⁡(x)−1664sin⁡(x)\frac{16 \sin^{2}{\left(x \right)} - 16 \sin{\left(x \right)} \cos{\left(x \right)} - 16}{64 \sin{\left(x \right)}} 
(-16 + 16*sin(x)^2 - 16*cos(x)*sin(x))/(64*sin(x))
Unión de expresiones racionales [src] 
        2                   
-1 + sin (x) - cos(x)*sin(x)
----------------------------
          4*sin(x)
sin⁡2(x)−sin⁡(x)cos⁡(x)−14sin⁡(x)\frac{\sin^{2}{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} - 1}{4 \sin{\left(x \right)}} 
(-1 + sin(x)^2 - cos(x)*sin(x))/(4*sin(x))
Abrimos la expresión [src] 
     1       cos(x)   sin(x)
- -------- - ------ + ------
  4*sin(x)     4        4
sin⁡(x)4−cos⁡(x)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
     1       sin(x)   cos(x)
- -------- + ------ - ------
  4*sin(x)     4        4
sin⁡(x)4−cos⁡(x)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
-1/(4*sin(x)) + sin(x)/4 - cos(x)/4
Compilar la expresión [src] 
     1       cos(x)   sin(x)
- -------- - ------ + ------
  4*sin(x)     4        4
sin⁡(x)4−cos⁡(x)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
-1/(4*sin(x)) - cos(x)/4 + sin(x)/4
Parte trigonométrica [src] 
               ___    /    pi\
             \/ 2 *cos|x + --|
     1                \    4 /
- -------- - -----------------
  4*sin(x)           4
−2cos⁡(x+π4)4−14sin⁡(x)- \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
               ___ /       2/x   pi\\
             \/ 2 *|1 - tan |- + --||
     1             \        \2   8 //
- -------- - ------------------------
  4*sin(x)       /       2/x   pi\\  
               4*|1 + tan |- + --||  
                 \        \2   8 //
−2(1−tan⁡2(x2+π8))4(tan⁡2(x2+π8)+1)−14sin⁡(x)- \frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}\right)}{4 \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)} - \frac{1}{4 \sin{\left(x \right)}} 
                /    pi\         
             sin|x + --|         
     1          \    2 /   sin(x)
- -------- - ----------- + ------
  4*sin(x)        4          4
sin⁡(x)4−sin⁡(x+π2)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
                /    pi\                
             sec|x - --|                
     1          \    2 /         1      
- -------- - ----------- + -------------
  4*sec(x)        4             /    pi\
                           4*sec|x - --|
                                \    2 /
−sec⁡(x−π2)4+14sec⁡(x−π2)−14sec⁡(x)- \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{4} + \frac{1}{4 \sec{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{4 \sec{\left(x \right)}} 
                 ___     
  csc(x)       \/ 2      
- ------ - --------------
    4           /     pi\
           4*csc|-x + --|
                \     4 /
−csc⁡(x)4−24csc⁡(−x+π4)- \frac{\csc{\left(x \right)}}{4} - \frac{\sqrt{2}}{4 \csc{\left(- x + \frac{\pi}{4} \right)}} 
 /    cos(x)\        
-|1 + ------|*cos(x) 
 \    sin(x)/        
---------------------
          4
−(1+cos⁡(x)sin⁡(x))cos⁡(x)4- \frac{\left(1 + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{4} 
               ___    /    3*pi\
             \/ 2 *sin|x + ----|
     1                \     4  /
- -------- - -------------------
  4*sin(x)            4
−2sin⁡(x+3π4)4−14sin⁡(x)- \frac{\sqrt{2} \sin{\left(x + \frac{3 \pi}{4} \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
     1       csc(x)      1    
- -------- - ------ + --------
  4*sec(x)     4      4*csc(x)
−csc⁡(x)4−14sec⁡(x)+14csc⁡(x)- \frac{\csc{\left(x \right)}}{4} - \frac{1}{4 \sec{\left(x \right)}} + \frac{1}{4 \csc{\left(x \right)}} 
     1       cos(x)   sin(x)
- -------- - ------ + ------
  4*sin(x)     4        4
sin⁡(x)4−cos⁡(x)4−14sin⁡(x)\frac{\sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
                              /    pi\
                           cos|x - --|
        1         cos(x)      \    2 /
- ------------- - ------ + -----------
       /    pi\     4           4     
  4*cos|x - --|                       
       \    2 /
−cos⁡(x)4+cos⁡(x−π2)4−14cos⁡(x−π2)- \frac{\cos{\left(x \right)}}{4} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{4} - \frac{1}{4 \cos{\left(x - \frac{\pi}{2} \right)}} 
     /    pi\                
  sec|x - --|         ___    
     \    2 /       \/ 2     
- ----------- - -------------
       4             /    pi\
                4*sec|x + --|
                     \    4 /
−sec⁡(x−π2)4−24sec⁡(x+π4)- \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{4} - \frac{\sqrt{2}}{4 \sec{\left(x + \frac{\pi}{4} \right)}} 
        /x\                2/x\            2/x\
     tan|-|         1 - tan |-|     1 + tan |-|
        \2/                 \2/             \2/
--------------- - --------------- - -----------
  /       2/x\\     /       2/x\\          /x\ 
2*|1 + tan |-||   4*|1 + tan |-||     8*tan|-| 
  \        \2//     \        \2//          \2/
−1−tan⁡2(x2)4(tan⁡2(x2)+1)−tan⁡2(x2)+18tan⁡(x2)+tan⁡(x2)2(tan⁡2(x2)+1)- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{4 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{8 \tan{\left(\frac{x}{2} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
               ___    2/x   pi\ /        2/x   pi\\
             \/ 2 *sin |- + --|*|-1 + cot |- + --||
     1                 \2   8 / \         \2   8 //
- -------- - --------------------------------------
  4*sin(x)                     4
−2(cot⁡2(x2+π8)−1)sin⁡2(x2+π8)4−14sin⁡(x)- \frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} - 1\right) \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{4} - \frac{1}{4 \sin{\left(x \right)}} 
         2/x\     ___ /       2/x   pi\\
  1 + tan |-|   \/ 2 *|1 - tan |- + --||
          \2/         \        \2   8 //
- ----------- - ------------------------
         /x\        /       2/x   pi\\  
    8*tan|-|      4*|1 + tan |- + --||  
         \2/        \        \2   8 //
−2(1−tan⁡2(x2+π8))4(tan⁡2(x2+π8)+1)−tan⁡2(x2)+18tan⁡(x2)- \frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}\right)}{4 \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)} - \frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{8 \tan{\left(\frac{x}{2} \right)}} 
             ___    /    pi\
           \/ 2 *cos|x + --|
  csc(x)            \    4 /
- ------ - -----------------
    4              4
−2cos⁡(x+π4)4−csc⁡(x)4- \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{4} - \frac{\csc{\left(x \right)}}{4} 
                    ___    /    pi\
                  \/ 2 *cos|x + --|
        1                  \    4 /
- ------------- - -----------------
       /    pi\           4        
  4*cos|x - --|                    
       \    2 /
−2cos⁡(x+π4)4−14cos⁡(x−π2)- \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{4} - \frac{1}{4 \cos{\left(x - \frac{\pi}{2} \right)}} 
        /x\                 2/x\           2/x\
     cot|-|         -1 + cot |-|    1 + cot |-|
        \2/                  \2/            \2/
--------------- - --------------- - -----------
  /       2/x\\     /       2/x\\          /x\ 
2*|1 + cot |-||   4*|1 + cot |-||     8*cot|-| 
  \        \2//     \        \2//          \2/
−cot⁡2(x2)−14(cot⁡2(x2)+1)−cot⁡2(x2)+18cot⁡(x2)+cot⁡(x2)2(cot⁡2(x2)+1)- \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{8 \cot{\left(\frac{x}{2} \right)}} + \frac{\cot{\left(\frac{x}{2} \right)}}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
        1         csc(x)      1    
- ------------- - ------ + --------
       /pi    \     4      4*csc(x)
  4*csc|-- - x|                    
       \2     /
−csc⁡(x)4−14csc⁡(−x+π2)+14csc⁡(x)- \frac{\csc{\left(x \right)}}{4} - \frac{1}{4 \csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{4 \csc{\left(x \right)}} 
         2/x\     ___ /        2/x   pi\\
  1 + cot |-|   \/ 2 *|-1 + cot |- + --||
          \2/         \         \2   8 //
- ----------- - -------------------------
         /x\         /       2/x   pi\\  
    8*cot|-|       4*|1 + cot |- + --||  
         \2/         \        \2   8 //
−cot⁡2(x2)+18cot⁡(x2)−2(cot⁡2(x2+π8)−1)4(cot⁡2(x2+π8)+1)- \frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{8 \cot{\left(\frac{x}{2} \right)}} - \frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} - 1\right)}{4 \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)} 
-(1 + cot(x/2)^2)/(8*cot(x/2)) - sqrt(2)*(-1 + cot(x/2 + pi/8)^2)/(4*(1 + cot(x/2 + pi/8)^2))
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