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Simplificación de expresiones/ Descomposición en fracciones simples/ atan((2*sin(x))/(1+cos(x)))/2

¿Cómo vas a descomponer esta atan((2*sin(x))/(1+cos(x)))/2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    / 2*sin(x) \
atan|----------|
    \1 + cos(x)/
----------------
       2
atan⁡(2sin⁡(x)cos⁡(x)+1)2\frac{\operatorname{atan}{\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}}{2} 
atan((2*sin(x))/(1 + cos(x)))/2
Descomposición de una fracción [src] 
atan((2*sin(x))/(1 + cos(x)))/2
atan⁡(2sin⁡(x)cos⁡(x)+1)2\frac{\operatorname{atan}{\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}}{2} 
    / 2*sin(x) \
atan|----------|
    \1 + cos(x)/
----------------
       2
Respuesta numérica [src] 
0.5*atan((2*sin(x))/(1 + cos(x)))
0.5*atan((2*sin(x))/(1 + cos(x)))
Potencias [src] 
     /  /   -I*x    I*x\\ 
     |I*\- e     + e   /| 
-atan|------------------| 
     |      I*x    -I*x | 
     |     e      e     | 
     | 1 + ---- + ----- | 
     \      2       2   / 
--------------------------
            2
−atan⁡(i(eix−e−ix)eix2+1+e−ix2)2- \frac{\operatorname{atan}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} \right)}}{2} 
-atan(i*(-exp(-i*x) + exp(i*x))/(1 + exp(i*x)/2 + exp(-i*x)/2))/2
Parte trigonométrica [src] 
    /    2*sin(x)   \
atan|---------------|
    |       /    pi\|
    |1 + sin|x + --||
    \       \    2 //
---------------------
          2
atan⁡(2sin⁡(x)sin⁡(x+π2)+1)2\frac{\operatorname{atan}{\left(\frac{2 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1} \right)}}{2} 
    /         2         \
atan|-------------------|
    |/      1   \       |
    ||1 + ------|*csc(x)|
    \\    sec(x)/       /
-------------------------
            2
atan⁡(2(1+1sec⁡(x))csc⁡(x))2\frac{\operatorname{atan}{\left(\frac{2}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} \right)}}{2} 
    /           2            \
atan|------------------------|
    |/      1   \    /    pi\|
    ||1 + ------|*sec|x - --||
    \\    sec(x)/    \    2 //
------------------------------
              2
atan⁡(2(1+1sec⁡(x))sec⁡(x−π2))2\frac{\operatorname{atan}{\left(\frac{2}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2} 
    /                 /x\           \
    |            4*tan|-|           |
    |                 \2/           |
atan|-------------------------------|
    |              /           2/x\\|
    |              |    1 - tan |-|||
    |/       2/x\\ |            \2/||
    ||1 + tan |-||*|1 + -----------||
    |\        \2// |           2/x\||
    |              |    1 + tan |-|||
    \              \            \2///
-------------------------------------
                  2
atan⁡(4tan⁡(x2)(1−tan⁡2(x2)tan⁡2(x2)+1+1)(tan⁡2(x2)+1))2\frac{\operatorname{atan}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} 
    /     /    pi\\
    |2*cos|x - --||
    |     \    2 /|
atan|-------------|
    \  1 + cos(x) /
-------------------
         2
atan⁡(2cos⁡(x−π2)cos⁡(x)+1)2\frac{\operatorname{atan}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1} \right)}}{2} 
    /           2            \
atan|------------------------|
    |/         1     \       |
    ||1 + -----------|*csc(x)|
    ||       /pi    \|       |
    ||    csc|-- - x||       |
    \\       \2     //       /
------------------------------
              2
atan⁡(2(1+1csc⁡(−x+π2))csc⁡(x))2\frac{\operatorname{atan}{\left(\frac{2}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{2} 
    /                 /x\            \
    |            4*cot|-|            |
    |                 \2/            |
atan|--------------------------------|
    |              /            2/x\\|
    |              |    -1 + cot |-|||
    |/       2/x\\ |             \2/||
    ||1 + cot |-||*|1 + ------------||
    |\        \2// |           2/x\ ||
    |              |    1 + cot |-| ||
    \              \            \2/ //
--------------------------------------
                  2
atan⁡(4cot⁡(x2)(cot⁡2(x2)−1cot⁡2(x2)+1+1)(cot⁡2(x2)+1))2\frac{\operatorname{atan}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} 
atan(4*cot(x/2)/((1 + cot(x/2)^2)*(1 + (-1 + cot(x/2)^2)/(1 + cot(x/2)^2))))/2
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