Sr Examen

Otras calculadoras

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)
Simplificación general [src] 
    /      ___    /    pi\\
    |1 + \/ 2 *sin|x + --||
    |             \    4 /|
atan|---------------------|
    \      1 + cos(x)     /
atan⁡(2sin⁡(x+π4)+1cos⁡(x)+1)\operatorname{atan}{\left(\frac{\sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)} + 1}{\cos{\left(x \right)} + 1} \right)} 
atan((1 + sqrt(2)*sin(x + pi/4))/(1 + cos(x)))
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)/
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)))
Potencias [src] 
     /        /   -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)} 
    /      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)))
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)))
Parte trigonométrica [src] 
    /               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)} 
    /         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)} 
    /       /    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)} 
    /                     /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)} 
    /                     /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)} 
    /             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 + ----------|
    \    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)} 
    /               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)))
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)))
Respuesta numérica [src] 
atan(((2*sin(x))/(1 + cos(x)) + 2)/2)
atan(((2*sin(x))/(1 + cos(x)) + 2)/2)
Denominador racional [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)))
    © Sr Examen – Калькулятор