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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    / 2*sin(x)     \
    |---------- - 2|
    |1 + cos(x)    |
atan|--------------|
    \      2       /
atan⁡(−2+2sin⁡(x)cos⁡(x)+12)\operatorname{atan}{\left(\frac{-2 + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2} \right)} 
atan(((2*sin(x))/(1 + cos(x)) - 2)/2)
Descomposición de una fracción [src] 
-atan(1 - sin(x)/(1 + cos(x)))
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
Simplificación general [src] 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
-atan(1 - sin(x)/(1 + cos(x)))
Unión de expresiones racionales [src] 
    /-1 - cos(x) + sin(x)\
atan|--------------------|
    \     1 + cos(x)     /
atan⁡(sin⁡(x)−cos⁡(x)−1cos⁡(x)+1)\operatorname{atan}{\left(\frac{\sin{\left(x \right)} - \cos{\left(x \right)} - 1}{\cos{\left(x \right)} + 1} \right)} 
atan((-1 - cos(x) + sin(x))/(1 + cos(x)))
Denominador racional [src] 
     /1 - sin(x) + cos(x)\
-atan|-------------------|
     \     1 + cos(x)    /
−atan⁡(−sin⁡(x)+cos⁡(x)+1cos⁡(x)+1)- \operatorname{atan}{\left(\frac{- \sin{\left(x \right)} + \cos{\left(x \right)} + 1}{\cos{\left(x \right)} + 1} \right)} 
-atan((1 - sin(x) + cos(x))/(1 + cos(x)))
Denominador común [src] 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
-atan(1 - sin(x)/(1 + cos(x)))
Abrimos la expresión [src] 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
-atan(1 - sin(x)/(1 + cos(x)))
Potencias [src] 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
     /       /   -I*x    I*x\ \
     |     I*\- e     + e   / |
-atan|1 + --------------------|
     |      /     I*x    -I*x\|
     |      |    e      e    ||
     |    2*|1 + ---- + -----||
     \      \     2       2  //
−atan⁡(i(eix−e−ix)2(eix2+1+e−ix2)+1)- \operatorname{atan}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}\right)} + 1 \right)} 
-atan(1 + i*(-exp(-i*x) + exp(i*x))/(2*(1 + exp(i*x)/2 + exp(-i*x)/2)))
Combinatoria [src] 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
-atan(1 - sin(x)/(1 + cos(x)))
Parte trigonométrica [src] 
     /                     /x\           \
     |                2*tan|-|           |
     |                     \2/           |
-atan|1 - -------------------------------|
     |                  /           2/x\\|
     |                  |    1 - tan |-|||
     |    /       2/x\\ |            \2/||
     |    |1 + tan |-||*|1 + -----------||
     |    \        \2// |           2/x\||
     |                  |    1 + tan |-|||
     \                  \            \2///
−atan⁡(1−2tan⁡(x2)(1−tan⁡2(x2)tan⁡2(x2)+1+1)(tan⁡2(x2)+1))- \operatorname{atan}{\left(1 - \frac{2 \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)} 
     /               1            \
-atan|1 - ------------------------|
     |    /      1   \    /    pi\|
     |    |1 + ------|*sec|x - --||
     \    \    sec(x)/    \    2 //
−atan⁡(1−1(1+1sec⁡(x))sec⁡(x−π2))- \operatorname{atan}{\left(1 - \frac{1}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)} 
     /                     /x\            \
     |                2*cot|-|            |
     |                     \2/            |
-atan|1 - --------------------------------|
     |                  /            2/x\\|
     |                  |    -1 + cot |-|||
     |    /       2/x\\ |             \2/||
     |    |1 + cot |-||*|1 + ------------||
     |    \        \2// |           2/x\ ||
     |                  |    1 + cot |-| ||
     \                  \            \2/ //
−atan⁡(1−2cot⁡(x2)(cot⁡2(x2)−1cot⁡2(x2)+1+1)(cot⁡2(x2)+1))- \operatorname{atan}{\left(1 - \frac{2 \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)} 
     /      sin(x)  \
-atan|1 - ----------|
     \    1 + cos(x)/
−atan⁡(1−sin⁡(x)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)} 
     /       /    pi\\
     |    cos|x - --||
     |       \    2 /|
-atan|1 - -----------|
     \     1 + cos(x)/
−atan⁡(1−cos⁡(x−π2)cos⁡(x)+1)- \operatorname{atan}{\left(1 - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1} \right)} 
     /             1         \
-atan|1 - -------------------|
     |    /      1   \       |
     |    |1 + ------|*csc(x)|
     \    \    sec(x)/       /
−atan⁡(1−1(1+1sec⁡(x))csc⁡(x))- \operatorname{atan}{\left(1 - \frac{1}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} \right)} 
     /         sin(x)    \
-atan|1 - ---------------|
     |           /    pi\|
     |    1 + sin|x + --||
     \           \    2 //
−atan⁡(1−sin⁡(x)sin⁡(x+π2)+1)- \operatorname{atan}{\left(1 - \frac{\sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1} \right)} 
     /               1            \
-atan|1 - ------------------------|
     |    /         1     \       |
     |    |1 + -----------|*csc(x)|
     |    |       /pi    \|       |
     |    |    csc|-- - x||       |
     \    \       \2     //       /
−atan⁡(1−1(1+1csc⁡(−x+π2))csc⁡(x))- \operatorname{atan}{\left(1 - \frac{1}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)} 
-atan(1 - 1/((1 + 1/csc(pi/2 - x))*csc(x)))
Respuesta numérica [src] 
atan(((2*sin(x))/(1 + cos(x)) - 2)/2)
atan(((2*sin(x))/(1 + cos(x)) - 2)/2)
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