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Simplificación de expresiones/ Descomposición en fracciones simples/ cot(p/(2-a))-tan(p+a)+sin(3*p/(2-a))/cos(p+a)

¿Cómo vas a descomponer esta cot(p/(2-a))-tan(p+a)+sin(3*p/(2-a))/cos(p+a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                             / 3*p \
                          sin|-----|
   /  p  \                   \2 - a/
cot|-----| - tan(p + a) + ----------
   \2 - a/                cos(p + a)
(−tan⁡(a+p)+cot⁡(p2−a))+sin⁡(3p2−a)cos⁡(a+p)\left(- \tan{\left(a + p \right)} + \cot{\left(\frac{p}{2 - a} \right)}\right) + \frac{\sin{\left(\frac{3 p}{2 - a} \right)}}{\cos{\left(a + p \right)}} 
cot(p/(2 - a)) - tan(p + a) + sin((3*p)/(2 - a))/cos(p + a)
Simplificación general [src] 
                                / 3*p  \
                             sin|------|
     /  p   \                   \-2 + a/
- cot|------| - tan(a + p) - -----------
     \-2 + a/                 cos(a + p)
−sin⁡(3pa−2)cos⁡(a+p)−tan⁡(a+p)−cot⁡(pa−2)- \frac{\sin{\left(\frac{3 p}{a - 2} \right)}}{\cos{\left(a + p \right)}} - \tan{\left(a + p \right)} - \cot{\left(\frac{p}{a - 2} \right)} 
-cot(p/(-2 + a)) - tan(a + p) - sin(3*p/(-2 + a))/cos(a + p)
Respuesta numérica [src] 
-tan(p + a) + sin((3*p)/(2 - a))/cos(p + a) + cot(p/(2 - a))
-tan(p + a) + sin((3*p)/(2 - a))/cos(p + a) + cot(p/(2 - a))
Unión de expresiones racionales [src] 
/                 /  p  \\                 / 3*p \
|-tan(a + p) + cot|-----||*cos(a + p) + sin|-----|
\                 \2 - a//                 \2 - a/
--------------------------------------------------
                    cos(a + p)
(−tan⁡(a+p)+cot⁡(p2−a))cos⁡(a+p)+sin⁡(3p2−a)cos⁡(a+p)\frac{\left(- \tan{\left(a + p \right)} + \cot{\left(\frac{p}{2 - a} \right)}\right) \cos{\left(a + p \right)} + \sin{\left(\frac{3 p}{2 - a} \right)}}{\cos{\left(a + p \right)}} 
((-tan(a + p) + cot(p/(2 - a)))*cos(a + p) + sin(3*p/(2 - a)))/cos(a + p)
Combinatoria [src] 
              /  p  \                              / 3*p \
cos(a + p)*cot|-----| - cos(a + p)*tan(a + p) + sin|-----|
              \2 - a/                              \2 - a/
----------------------------------------------------------
                        cos(a + p)
sin⁡(3p2−a)−cos⁡(a+p)tan⁡(a+p)+cos⁡(a+p)cot⁡(p2−a)cos⁡(a+p)\frac{\sin{\left(\frac{3 p}{2 - a} \right)} - \cos{\left(a + p \right)} \tan{\left(a + p \right)} + \cos{\left(a + p \right)} \cot{\left(\frac{p}{2 - a} \right)}}{\cos{\left(a + p \right)}} 
(cos(a + p)*cot(p/(2 - a)) - cos(a + p)*tan(a + p) + sin(3*p/(2 - a)))/cos(a + p)
Denominador común [src] 
                 / 3*p \             
              sin|-----|             
                 \2 - a/      /  p  \
-tan(a + p) + ---------- + cot|-----|
              cos(a + p)      \2 - a/
sin⁡(3p2−a)cos⁡(a+p)−tan⁡(a+p)+cot⁡(p2−a)\frac{\sin{\left(\frac{3 p}{2 - a} \right)}}{\cos{\left(a + p \right)}} - \tan{\left(a + p \right)} + \cot{\left(\frac{p}{2 - a} \right)} 
-tan(a + p) + sin(3*p/(2 - a))/cos(a + p) + cot(p/(2 - a))
Potencias [src] 
                 / 3*p \             
              sin|-----|             
                 \2 - a/      /  p  \
-tan(a + p) + ---------- + cot|-----|
              cos(a + p)      \2 - a/
sin⁡(3p2−a)cos⁡(a+p)−tan⁡(a+p)+cot⁡(p2−a)\frac{\sin{\left(\frac{3 p}{2 - a} \right)}}{\cos{\left(a + p \right)}} - \tan{\left(a + p \right)} + \cot{\left(\frac{p}{2 - a} \right)} 
                                        /   -3*I*p    3*I*p\                
                                        |   ------    -----|                
    /   I*(a + p)    I*(-a - p)\        |   2 - a     2 - a|                
  I*\- e          + e          /      I*\- e       + e     /         /  p  \
- ------------------------------ - ---------------------------- + cot|-----|
      I*(a + p)    I*(-a - p)        / I*(a + p)    I*(-a - p)\      \2 - a/
     e          + e                  |e            e          |             
                                   2*|---------- + -----------|             
                                     \    2             2     /
−i(ei(−a−p)−ei(a+p))ei(−a−p)+ei(a+p)+cot⁡(p2−a)−i(e3ip2−a−e−3ip2−a)2(ei(−a−p)2+ei(a+p)2)- \frac{i \left(e^{i \left(- a - p\right)} - e^{i \left(a + p\right)}\right)}{e^{i \left(- a - p\right)} + e^{i \left(a + p\right)}} + \cot{\left(\frac{p}{2 - a} \right)} - \frac{i \left(e^{\frac{3 i p}{2 - a}} - e^{- \frac{3 i p}{2 - a}}\right)}{2 \left(\frac{e^{i \left(- a - p\right)}}{2} + \frac{e^{i \left(a + p\right)}}{2}\right)} 
-i*(-exp(i*(a + p)) + exp(i*(-a - p)))/(exp(i*(a + p)) + exp(i*(-a - p))) - i*(-exp(-3*i*p/(2 - a)) + exp(3*i*p/(2 - a)))/(2*(exp(i*(a + p))/2 + exp(i*(-a - p))/2)) + cot(p/(2 - a))
Denominador racional [src] 
     / 3*p  \                 /  p   \                        
- sin|------| - cos(a + p)*cot|------| - cos(a + p)*tan(a + p)
     \-2 + a/                 \-2 + a/                        
--------------------------------------------------------------
                          cos(a + p)
−sin⁡(3pa−2)−cos⁡(a+p)tan⁡(a+p)−cos⁡(a+p)cot⁡(pa−2)cos⁡(a+p)\frac{- \sin{\left(\frac{3 p}{a - 2} \right)} - \cos{\left(a + p \right)} \tan{\left(a + p \right)} - \cos{\left(a + p \right)} \cot{\left(\frac{p}{a - 2} \right)}}{\cos{\left(a + p \right)}} 
(-sin(3*p/(-2 + a)) - cos(a + p)*cot(p/(-2 + a)) - cos(a + p)*tan(a + p))/cos(a + p)
Compilar la expresión [src] 
                 / 3*p \             
              sin|-----|             
                 \2 - a/      /  p  \
-tan(p + a) + ---------- + cot|-----|
              cos(p + a)      \2 - a/
sin⁡(3p2−a)cos⁡(a+p)−tan⁡(a+p)+cot⁡(p2−a)\frac{\sin{\left(\frac{3 p}{2 - a} \right)}}{\cos{\left(a + p \right)}} - \tan{\left(a + p \right)} + \cot{\left(\frac{p}{2 - a} \right)} 
-tan(p + a) + sin((3*p)/(2 - a))/cos(p + a) + cot(p/(2 - a))
Abrimos la expresión [src] 
             / 3*p \                                                              
          sin|-----|                                                              
             \2 - a/                  tan(a)              tan(p)           /  p  \
----------------------------- - ----------------- - ----------------- + cot|-----|
cos(a)*cos(p) - sin(a)*sin(p)   1 - tan(a)*tan(p)   1 - tan(a)*tan(p)      \2 - a/
cot⁡(p2−a)−tan⁡(a)−tan⁡(a)tan⁡(p)+1−tan⁡(p)−tan⁡(a)tan⁡(p)+1+sin⁡(3p2−a)−sin⁡(a)sin⁡(p)+cos⁡(a)cos⁡(p)\cot{\left(\frac{p}{2 - a} \right)} - \frac{\tan{\left(a \right)}}{- \tan{\left(a \right)} \tan{\left(p \right)} + 1} - \frac{\tan{\left(p \right)}}{- \tan{\left(a \right)} \tan{\left(p \right)} + 1} + \frac{\sin{\left(\frac{3 p}{2 - a} \right)}}{- \sin{\left(a \right)} \sin{\left(p \right)} + \cos{\left(a \right)} \cos{\left(p \right)}} 
sin((3*p)/(2 - a))/(cos(a)*cos(p) - sin(a)*sin(p)) - tan(a)/(1 - tan(a)*tan(p)) - tan(p)/(1 - tan(a)*tan(p)) + cot(p/(2 - a))
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