Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(t)/(1+sin(t))+cos(t)/(1-sin(t))

¿Cómo vas a descomponer esta cos(t)/(1+sin(t))+cos(t)/(1-sin(t)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  cos(t)       cos(t)  
---------- + ----------
1 + sin(t)   1 - sin(t)
cos⁡(t)sin⁡(t)+1+cos⁡(t)1−sin⁡(t)\frac{\cos{\left(t \right)}}{\sin{\left(t \right)} + 1} + \frac{\cos{\left(t \right)}}{1 - \sin{\left(t \right)}} 
cos(t)/(1 + sin(t)) + cos(t)/(1 - sin(t))
Simplificación general [src] 
  2   
------
cos(t)
2cos⁡(t)\frac{2}{\cos{\left(t \right)}} 
2/cos(t)
Denominador racional [src] 
(1 - sin(t))*cos(t) + (1 + sin(t))*cos(t)
-----------------------------------------
        (1 - sin(t))*(1 + sin(t))
(1−sin⁡(t))cos⁡(t)+(sin⁡(t)+1)cos⁡(t)(1−sin⁡(t))(sin⁡(t)+1)\frac{\left(1 - \sin{\left(t \right)}\right) \cos{\left(t \right)} + \left(\sin{\left(t \right)} + 1\right) \cos{\left(t \right)}}{\left(1 - \sin{\left(t \right)}\right) \left(\sin{\left(t \right)} + 1\right)} 
((1 - sin(t))*cos(t) + (1 + sin(t))*cos(t))/((1 - sin(t))*(1 + sin(t)))
Denominador común [src] 
 -2*cos(t)  
------------
        2   
-1 + sin (t)
−2cos⁡(t)sin⁡2(t)−1- \frac{2 \cos{\left(t \right)}}{\sin^{2}{\left(t \right)} - 1} 
-2*cos(t)/(-1 + sin(t)^2)
Respuesta numérica [src] 
cos(t)/(1.0 - sin(t)) + cos(t)/(1.0 + sin(t))
cos(t)/(1.0 - sin(t)) + cos(t)/(1.0 + sin(t))
Unión de expresiones racionales [src] 
         2*cos(t)        
-------------------------
(1 - sin(t))*(1 + sin(t))
2cos⁡(t)(1−sin⁡(t))(sin⁡(t)+1)\frac{2 \cos{\left(t \right)}}{\left(1 - \sin{\left(t \right)}\right) \left(\sin{\left(t \right)} + 1\right)} 
2*cos(t)/((1 - sin(t))*(1 + sin(t)))
Potencias [src] 
      I*t    -I*t              I*t    -I*t     
     e      e                 e      e         
     ---- + -----             ---- + -----     
      2       2                2       2       
---------------------- + ----------------------
      /   -I*t    I*t\         /   -I*t    I*t\
    I*\- e     + e   /       I*\- e     + e   /
1 + ------------------   1 - ------------------
            2                        2
eit2+e−it2i(eit−e−it)2+1+eit2+e−it2−i(eit−e−it)2+1\frac{\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}}{\frac{i \left(e^{i t} - e^{- i t}\right)}{2} + 1} + \frac{\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}}{- \frac{i \left(e^{i t} - e^{- i t}\right)}{2} + 1} 
(exp(i*t)/2 + exp(-i*t)/2)/(1 + i*(-exp(-i*t) + exp(i*t))/2) + (exp(i*t)/2 + exp(-i*t)/2)/(1 - i*(-exp(-i*t) + exp(i*t))/2)
Combinatoria [src] 
        -2*cos(t)         
--------------------------
(1 + sin(t))*(-1 + sin(t))
−2cos⁡(t)(sin⁡(t)−1)(sin⁡(t)+1)- \frac{2 \cos{\left(t \right)}}{\left(\sin{\left(t \right)} - 1\right) \left(\sin{\left(t \right)} + 1\right)} 
-2*cos(t)/((1 + sin(t))*(-1 + sin(t)))
Parte trigonométrica [src] 
                  2/t\                              2/t\         
          -1 + cot |-|                      -1 + cot |-|         
                   \2/                               \2/         
------------------------------- + -------------------------------
              /           /t\ \                 /           /t\ \
              |      2*cot|-| |                 |      2*cot|-| |
/       2/t\\ |           \2/ |   /       2/t\\ |           \2/ |
|1 + cot |-||*|1 - -----------|   |1 + cot |-||*|1 + -----------|
\        \2// |           2/t\|   \        \2// |           2/t\|
              |    1 + cot |-||                 |    1 + cot |-||
              \            \2//                 \            \2//
cot⁡2(t2)−1(1+2cot⁡(t2)cot⁡2(t2)+1)(cot⁡2(t2)+1)+cot⁡2(t2)−1(1−2cot⁡(t2)cot⁡2(t2)+1)(cot⁡2(t2)+1)\frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\left(1 + \frac{2 \cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)} + \frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\left(1 - \frac{2 \cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)} 
2*sec(t)
2sec⁡(t)2 \sec{\left(t \right)} 
     2     
-----------
   /    pi\
sin|t + --|
   \    2 /
2sin⁡(t+π2)\frac{2}{\sin{\left(t + \frac{\pi}{2} \right)}} 
  /       2/t\\
2*|1 + cot |-||
  \        \2//
---------------
          2/t\ 
  -1 + cot |-| 
           \2/
2(cot⁡2(t2)+1)cot⁡2(t2)−1\frac{2 \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)}{\cot^{2}{\left(\frac{t}{2} \right)} - 1} 
               4               
-------------------------------
/          1      \    /pi    \
|1 + -------------|*csc|-- - t|
|       /pi      \|    \2     /
|    csc|-- - 2*t||            
\       \2       //
4(1+1csc⁡(−2t+π2))csc⁡(−t+π2)\frac{4}{\left(1 + \frac{1}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}}\right) \csc{\left(- t + \frac{\pi}{2} \right)}} 
         1                     1         
------------------- + -------------------
/      1   \          /      1   \       
|1 + ------|*sec(t)   |1 - ------|*sec(t)
\    csc(t)/          \    csc(t)/
1(1+1csc⁡(t))sec⁡(t)+1(1−1csc⁡(t))sec⁡(t)\frac{1}{\left(1 + \frac{1}{\csc{\left(t \right)}}\right) \sec{\left(t \right)}} + \frac{1}{\left(1 - \frac{1}{\csc{\left(t \right)}}\right) \sec{\left(t \right)}} 
  /         2/t\\
2*|1 - 2*sin |-||
  \          \2//
-----------------
        2        
     cos (t)
2(1−2sin⁡2(t2))cos⁡2(t)\frac{2 \left(1 - 2 \sin^{2}{\left(\frac{t}{2} \right)}\right)}{\cos^{2}{\left(t \right)}} 
     cos(t)            cos(t)    
--------------- + ---------------
       /    pi\          /    pi\
1 - cos|t - --|   1 + cos|t - --|
       \    2 /          \    2 /
cos⁡(t)cos⁡(t−π2)+1+cos⁡(t)1−cos⁡(t−π2)\frac{\cos{\left(t \right)}}{\cos{\left(t - \frac{\pi}{2} \right)} + 1} + \frac{\cos{\left(t \right)}}{1 - \cos{\left(t - \frac{\pi}{2} \right)}} 
          /        2/t\\        
        4*|-1 + cot |-||        
          \         \2//        
--------------------------------
              /            2   \
/       2/t\\ |    -1 + cot (t)|
|1 + cot |-||*|1 + ------------|
\        \2// |           2    |
              \    1 + cot (t) /
4(cot⁡2(t2)−1)(cot⁡2(t)−1cot⁡2(t)+1+1)(cot⁡2(t2)+1)\frac{4 \left(\cot^{2}{\left(\frac{t}{2} \right)} - 1\right)}{\left(\frac{\cot^{2}{\left(t \right)} - 1}{\cot^{2}{\left(t \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)} 
   /    pi\      /    pi\
sin|t + --|   sin|t + --|
   \    2 /      \    2 /
----------- + -----------
 1 - sin(t)    1 + sin(t)
sin⁡(t+π2)sin⁡(t)+1+sin⁡(t+π2)1−sin⁡(t)\frac{\sin{\left(t + \frac{\pi}{2} \right)}}{\sin{\left(t \right)} + 1} + \frac{\sin{\left(t + \frac{\pi}{2} \right)}}{1 - \sin{\left(t \right)}} 
     /pi    \
2*csc|-- - t|
     \2     /
2csc⁡(−t+π2)2 \csc{\left(- t + \frac{\pi}{2} \right)} 
  2   
------
cos(t)
2cos⁡(t)\frac{2}{\cos{\left(t \right)}} 
          /       2/t\\        
        4*|1 - tan |-||        
          \        \2//        
-------------------------------
              /           2   \
/       2/t\\ |    1 - tan (t)|
|1 + tan |-||*|1 + -----------|
\        \2// |           2   |
              \    1 + tan (t)/
4(1−tan⁡2(t2))(1−tan⁡2(t)tan⁡2(t)+1+1)(tan⁡2(t2)+1)\frac{4 \left(1 - \tan^{2}{\left(\frac{t}{2} \right)}\right)}{\left(\frac{1 - \tan^{2}{\left(t \right)}}{\tan^{2}{\left(t \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)} 
           1                          1            
------------------------ + ------------------------
/      1   \    /pi    \   /      1   \    /pi    \
|1 + ------|*csc|-- - t|   |1 - ------|*csc|-- - t|
\    csc(t)/    \2     /   \    csc(t)/    \2     /
1(1+1csc⁡(t))csc⁡(−t+π2)+1(1−1csc⁡(t))csc⁡(−t+π2)\frac{1}{\left(1 + \frac{1}{\csc{\left(t \right)}}\right) \csc{\left(- t + \frac{\pi}{2} \right)}} + \frac{1}{\left(1 - \frac{1}{\csc{\left(t \right)}}\right) \csc{\left(- t + \frac{\pi}{2} \right)}} 
  4*cos(t)  
------------
1 + cos(2*t)
4cos⁡(t)cos⁡(2t)+1\frac{4 \cos{\left(t \right)}}{\cos{\left(2 t \right)} + 1} 
           1                          1            
------------------------ + ------------------------
/         1     \          /         1     \       
|1 + -----------|*sec(t)   |1 - -----------|*sec(t)
|       /    pi\|          |       /    pi\|       
|    sec|t - --||          |    sec|t - --||       
\       \    2 //          \       \    2 //
1(1+1sec⁡(t−π2))sec⁡(t)+1(1−1sec⁡(t−π2))sec⁡(t)\frac{1}{\left(1 + \frac{1}{\sec{\left(t - \frac{\pi}{2} \right)}}\right) \sec{\left(t \right)}} + \frac{1}{\left(1 - \frac{1}{\sec{\left(t - \frac{\pi}{2} \right)}}\right) \sec{\left(t \right)}} 
                 2/t\                              2/t\          
          1 - tan |-|                       1 - tan |-|          
                  \2/                               \2/          
------------------------------- + -------------------------------
              /           /t\ \                 /           /t\ \
              |      2*tan|-| |                 |      2*tan|-| |
/       2/t\\ |           \2/ |   /       2/t\\ |           \2/ |
|1 + tan |-||*|1 - -----------|   |1 + tan |-||*|1 + -----------|
\        \2// |           2/t\|   \        \2// |           2/t\|
              |    1 + tan |-||                 |    1 + tan |-||
              \            \2//                 \            \2//
1−tan⁡2(t2)(1+2tan⁡(t2)tan⁡2(t2)+1)(tan⁡2(t2)+1)+1−tan⁡2(t2)(1−2tan⁡(t2)tan⁡2(t2)+1)(tan⁡2(t2)+1)\frac{1 - \tan^{2}{\left(\frac{t}{2} \right)}}{\left(1 + \frac{2 \tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)} + \frac{1 - \tan^{2}{\left(\frac{t}{2} \right)}}{\left(1 - \frac{2 \tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)} 
          4          
---------------------
/       1    \       
|1 + --------|*sec(t)
\    sec(2*t)/
4(1+1sec⁡(2t))sec⁡(t)\frac{4}{\left(1 + \frac{1}{\sec{\left(2 t \right)}}\right) \sec{\left(t \right)}} 
  /       2/t\\
2*|1 + tan |-||
  \        \2//
---------------
         2/t\  
  1 - tan |-|  
          \2/
2(tan⁡2(t2)+1)1−tan⁡2(t2)\frac{2 \left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)}{1 - \tan^{2}{\left(\frac{t}{2} \right)}} 
       /    pi\  
  4*sin|t + --|  
       \    2 /  
-----------------
       /pi      \
1 + sin|-- + 2*t|
       \2       /
4sin⁡(t+π2)sin⁡(2t+π2)+1\frac{4 \sin{\left(t + \frac{\pi}{2} \right)}}{\sin{\left(2 t + \frac{\pi}{2} \right)} + 1} 
4*sin(t + pi/2)/(1 + sin(pi/2 + 2*t))
    © Sr Examen – Калькулятор