Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(t)*cot(t)/((cos(t)*tan(t)))

¿Cómo vas a descomponer esta sin(t)*cot(t)/((cos(t)*tan(t))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(t)*cot(t)
-------------
cos(t)*tan(t)
sin⁡(t)cot⁡(t)cos⁡(t)tan⁡(t)\frac{\sin{\left(t \right)} \cot{\left(t \right)}}{\cos{\left(t \right)} \tan{\left(t \right)}} 
(sin(t)*cot(t))/((cos(t)*tan(t)))
Simplificación general [src] 
  1   
------
tan(t)
1tan⁡(t)\frac{1}{\tan{\left(t \right)}} 
1/tan(t)
Respuesta numérica [src] 
cot(t)*sin(t)/(cos(t)*tan(t))
cot(t)*sin(t)/(cos(t)*tan(t))
Potencias [src] 
 /   -I*t    I*t\ / I*t    -I*t\        
-\- e     + e   /*\e    + e    /*cot(t) 
----------------------------------------
     / I*t    -I*t\                     
     |e      e    | /   I*t    -I*t\    
   2*|---- + -----|*\- e    + e    /    
     \ 2       2  /
−(eit−e−it)(eit+e−it)cot⁡(t)2(−eit+e−it)(eit2+e−it2)- \frac{\left(e^{i t} - e^{- i t}\right) \left(e^{i t} + e^{- i t}\right) \cot{\left(t \right)}}{2 \left(- e^{i t} + e^{- i t}\right) \left(\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}\right)} 
-(-exp(-i*t) + exp(i*t))*(exp(i*t) + exp(-i*t))*cot(t)/(2*(exp(i*t)/2 + exp(-i*t)/2)*(-exp(i*t) + exp(-i*t)))
Parte trigonométrica [src] 
      1            cos(2*t)  
------------- + -------------
   /      pi\      /      pi\
cos|2*t - --|   cos|2*t - --|
   \      2 /      \      2 /
cos⁡(2t)cos⁡(2t−π2)+1cos⁡(2t−π2)\frac{\cos{\left(2 t \right)}}{\cos{\left(2 t - \frac{\pi}{2} \right)}} + \frac{1}{\cos{\left(2 t - \frac{\pi}{2} \right)}} 
       2              
1 + cot (t)           
----------- + cot(2*t)
  2*cot(t)
cot⁡2(t)+12cot⁡(t)+cot⁡(2t)\frac{\cot^{2}{\left(t \right)} + 1}{2 \cot{\left(t \right)}} + \cot{\left(2 t \right)} 
   1          1    
-------- + --------
sin(2*t)   tan(2*t)
1tan⁡(2t)+1sin⁡(2t)\frac{1}{\tan{\left(2 t \right)}} + \frac{1}{\sin{\left(2 t \right)}} 
   csc(t)  
-----------
   /pi    \
csc|-- - t|
   \2     /
csc⁡(t)csc⁡(−t+π2)\frac{\csc{\left(t \right)}}{\csc{\left(- t + \frac{\pi}{2} \right)}} 
   1         sin(4*t) 
-------- + -----------
sin(2*t)        2     
           2*sin (2*t)
1sin⁡(2t)+sin⁡(4t)2sin⁡2(2t)\frac{1}{\sin{\left(2 t \right)}} + \frac{\sin{\left(4 t \right)}}{2 \sin^{2}{\left(2 t \right)}} 
      2         
   sin (2*t)    
----------------
            3   
4*cos(t)*sin (t)
sin⁡2(2t)4sin⁡3(t)cos⁡(t)\frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{3}{\left(t \right)} \cos{\left(t \right)}} 
   /      pi\                
sec|2*t - --|                
   \      2 /      /      pi\
------------- + sec|2*t - --|
   sec(2*t)        \      2 /
sec⁡(2t−π2)+sec⁡(2t−π2)sec⁡(2t)\sec{\left(2 t - \frac{\pi}{2} \right)} + \frac{\sec{\left(2 t - \frac{\pi}{2} \right)}}{\sec{\left(2 t \right)}} 
cot(t)
cot⁡(t)\cot{\left(t \right)} 
     2       /t\
2*cot (t)*cot|-|
             \2/
----------------
          2/t\  
  -1 + cot |-|  
           \2/
2cot⁡(t2)cot⁡2(t)cot⁡2(t2)−1\frac{2 \cot{\left(\frac{t}{2} \right)} \cot^{2}{\left(t \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} - 1} 
   /    pi\
sec|t - --|
   \    2 /
-----------
   sec(t)
sec⁡(t−π2)sec⁡(t)\frac{\sec{\left(t - \frac{\pi}{2} \right)}}{\sec{\left(t \right)}} 
csc(t)
------
sec(t)
csc⁡(t)sec⁡(t)\frac{\csc{\left(t \right)}}{\sec{\left(t \right)}} 
   cos(t)  
-----------
   /    pi\
cos|t - --|
   \    2 /
cos⁡(t)cos⁡(t−π2)\frac{\cos{\left(t \right)}}{\cos{\left(t - \frac{\pi}{2} \right)}} 
   1               
-------- + csc(2*t)
tan(2*t)
csc⁡(2t)+1tan⁡(2t)\csc{\left(2 t \right)} + \frac{1}{\tan{\left(2 t \right)}} 
  1   
------
tan(t)
1tan⁡(t)\frac{1}{\tan{\left(t \right)}} 
            /t\      
       2*tan|-|      
            \2/      
---------------------
/       2/t\\    2   
|1 - tan |-||*tan (t)
\        \2//
2tan⁡(t2)(1−tan⁡2(t2))tan⁡2(t)\frac{2 \tan{\left(\frac{t}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{t}{2} \right)}\right) \tan^{2}{\left(t \right)}} 
 sin(2*t)
---------
     2   
2*sin (t)
sin⁡(2t)2sin⁡2(t)\frac{\sin{\left(2 t \right)}}{2 \sin^{2}{\left(t \right)}} 
cos(t)
------
sin(t)
cos⁡(t)sin⁡(t)\frac{\cos{\left(t \right)}}{\sin{\left(t \right)}} 
   csc(2*t)             
------------- + csc(2*t)
   /pi      \           
csc|-- - 2*t|           
   \2       /
csc⁡(2t)+csc⁡(2t)csc⁡(−2t+π2)\csc{\left(2 t \right)} + \frac{\csc{\left(2 t \right)}}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}} 
         2           
      sin (2*t)      
---------------------
     3       /    pi\
4*sin (t)*sin|t + --|
             \    2 /
sin⁡2(2t)4sin⁡3(t)sin⁡(t+π2)\frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{3}{\left(t \right)} \sin{\left(t + \frac{\pi}{2} \right)}} 
                  2   
   1       1 + tan (t)
-------- + -----------
tan(2*t)     2*tan(t)
tan⁡2(t)+12tan⁡(t)+1tan⁡(2t)\frac{\tan^{2}{\left(t \right)} + 1}{2 \tan{\left(t \right)}} + \frac{1}{\tan{\left(2 t \right)}} 
1/tan(2*t) + (1 + tan(t)^2)/(2*tan(t))
    © Sr Examen – Калькулятор