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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(90+a)*cos(270+a)*cos(a)/((cos(-180+a)*(-sin(-270+a))))

¿Cómo vas a descomponer esta tan(90+a)*cos(270+a)*cos(a)/((cos(-180+a)*(-sin(-270+a)))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
tan(90 + a)*cos(270 + a)*cos(a)
-------------------------------
 cos(-180 + a)*(-sin(-270 + a))
cos⁡(a+270)tan⁡(a+90)cos⁡(a)−sin⁡(a−270)cos⁡(a−180)\frac{\cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)} \cos{\left(a \right)}}{- \sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
((tan(90 + a)*cos(270 + a))*cos(a))/((cos(-180 + a)*(-sin(-270 + a))))
Simplificación general [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
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   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Respuesta numérica [src] 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Denominador común [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
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   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Combinatoria [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
---------------------------------
   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Unión de expresiones racionales [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
---------------------------------
   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Denominador racional [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
---------------------------------
   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Compilar la expresión [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
---------------------------------
   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
-cos(a)*cos(270 + a)*tan(90 + a)/(cos(-180 + a)*sin(-270 + a))
Potencias [src] 
-cos(a)*cos(270 + a)*tan(90 + a) 
---------------------------------
   cos(-180 + a)*sin(-270 + a)
−cos⁡(a)cos⁡(a+270)tan⁡(a+90)sin⁡(a−270)cos⁡(a−180)- \frac{\cos{\left(a \right)} \cos{\left(a + 270 \right)} \tan{\left(a + 90 \right)}}{\sin{\left(a - 270 \right)} \cos{\left(a - 180 \right)}} 
         / I*a    -I*a\ / I*(-270 - a)    I*(270 + a)\                                      
         |e      e    | |e               e           | /   I*(90 + a)    I*(-90 - a)\       
       2*|---- + -----|*|------------- + ------------|*\- e           + e           /       
         \ 2       2  / \      2              2      /                                      
--------------------------------------------------------------------------------------------
/ I*(-180 + a)    I*(180 - a)\                                                              
|e               e           | /   I*(270 - a)    I*(-270 + a)\ / I*(-90 - a)    I*(90 + a)\
|------------- + ------------|*\- e            + e            /*\e            + e          /
\      2              2      /
2(eia2+e−ia2)(ei(−a−270)2+ei(a+270)2)(ei(−a−90)−ei(a+90))(ei(180−a)2+ei(a−180)2)(−ei(270−a)+ei(a−270))(ei(−a−90)+ei(a+90))\frac{2 \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right) \left(\frac{e^{i \left(- a - 270\right)}}{2} + \frac{e^{i \left(a + 270\right)}}{2}\right) \left(e^{i \left(- a - 90\right)} - e^{i \left(a + 90\right)}\right)}{\left(\frac{e^{i \left(180 - a\right)}}{2} + \frac{e^{i \left(a - 180\right)}}{2}\right) \left(- e^{i \left(270 - a\right)} + e^{i \left(a - 270\right)}\right) \left(e^{i \left(- a - 90\right)} + e^{i \left(a + 90\right)}\right)} 
2*(exp(i*a)/2 + exp(-i*a)/2)*(exp(i*(-270 - a))/2 + exp(i*(270 + a))/2)*(-exp(i*(90 + a)) + exp(i*(-90 - a)))/((exp(i*(-180 + a))/2 + exp(i*(180 - a))/2)*(-exp(i*(270 - a)) + exp(i*(-270 + a)))*(exp(i*(-90 - a)) + exp(i*(90 + a))))
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