¿Cómo vas a descomponer esta cos(t)/(2*sqrt(sin(t))) expresión en fracciones?

Solución

Ha introducido [src]

   cos(t)   
------------
    ________
2*\/ sin(t)

\frac{\cos{\left(t \right)}}{2 \sqrt{\sin{\left(t \right)}}}

cos(t)/((2*sqrt(sin(t))))

Respuesta numérica [src]

0.5*sin(t)^(-0.5)*cos(t)

0.5*sin(t)^(-0.5)*cos(t)

Denominador racional [src]

  ________       
\/ sin(t) *cos(t)
-----------------
     2*sin(t)

\frac{\sqrt{\sin{\left(t \right)}} \cos{\left(t \right)}}{2 \sin{\left(t \right)}}

sqrt(sin(t))*cos(t)/(2*sin(t))

Potencias [src]

         / I*t    -I*t\   
     ___ |e      e    |   
   \/ 2 *|---- + -----|   
         \ 2       2  /   
--------------------------
     _____________________
    /    /   -I*t    I*t\ 
2*\/  -I*\- e     + e   /

\frac{\sqrt{2} \left(\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}\right)}{2 \sqrt{- i \left(e^{i t} - e^{- i t}\right)}}

sqrt(2)*(exp(i*t)/2 + exp(-i*t)/2)/(2*sqrt(-i*(-exp(-i*t) + exp(i*t))))

Parte trigonométrica [src]

      /           2/t\   \
      |      8*cot |-|   |
  ___ |            \4/   |
\/ 2 *|1 - --------------|
      |                 2|
      |    /       2/t\\ |
      |    |1 + cot |-|| |
      \    \        \4// /
--------------------------
           _____________  
          /       /t\     
         /     cot|-|     
        /         \2/     
 4*    /    -----------   
      /            2/t\   
     /      1 + cot |-|   
   \/               \2/

\frac{\sqrt{2} \left(1 - \frac{8 \cot^{2}{\left(\frac{t}{4} \right)}}{\left(\cot^{2}{\left(\frac{t}{4} \right)} + 1\right)^{2}}\right)}{4 \sqrt{\frac{\cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1}}}

        2     
 1 - -------  
        2/t\  
     csc |-|  
         \2/  
--------------
      ________
     /   1    
2*  /  ------ 
  \/   csc(t)

\frac{1 - \frac{2}{\csc^{2}{\left(\frac{t}{2} \right)}}}{2 \sqrt{\frac{1}{\csc{\left(t \right)}}}}

   /    pi\ 
sin|t + --| 
   \    2 / 
------------
    ________
2*\/ sin(t)

\frac{\sin{\left(t + \frac{\pi}{2} \right)}}{2 \sqrt{\sin{\left(t \right)}}}

       cos(t)      
-------------------
      _____________
     /    /    pi\ 
2*  /  cos|t - --| 
  \/      \    2 /

\frac{\cos{\left(t \right)}}{2 \sqrt{\cos{\left(t - \frac{\pi}{2} \right)}}}

      /           2/t\   \
      |      8*tan |-|   |
  ___ |            \4/   |
\/ 2 *|1 - --------------|
      |                 2|
      |    /       2/t\\ |
      |    |1 + tan |-|| |
      \    \        \4// /
--------------------------
           _____________  
          /       /t\     
         /     tan|-|     
        /         \2/     
 4*    /    -----------   
      /            2/t\   
     /      1 + tan |-|   
   \/               \2/

\frac{\sqrt{2} \left(1 - \frac{8 \tan^{2}{\left(\frac{t}{4} \right)}}{\left(\tan^{2}{\left(\frac{t}{4} \right)} + 1\right)^{2}}\right)}{4 \sqrt{\frac{\tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1}}}

            2        
   1 - ------------  
          2/t   pi\  
       sec |- - --|  
           \2   2 /  
---------------------
        _____________
       /      1      
2*    /  ----------- 
     /      /    pi\ 
    /    sec|t - --| 
  \/        \    2 /

\frac{1 - \frac{2}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}}{2 \sqrt{\frac{1}{\sec{\left(t - \frac{\pi}{2} \right)}}}}

          1          
---------------------
      ________       
     /   1           
2*  /  ------ *sec(t)
  \/   csc(t)

\frac{1}{2 \sqrt{\frac{1}{\csc{\left(t \right)}}} \sec{\left(t \right)}}

           ___ /       2/t\\         
         \/ 2 *|1 - tan |-||         
               \        \2//         
-------------------------------------
          _____________              
         /       /t\                 
        /     tan|-|                 
       /         \2/    /       2/t\\
4*    /    ----------- *|1 + tan |-||
     /            2/t\  \        \2//
    /      1 + tan |-|               
  \/               \2/

\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{t}{2} \right)}\right)}{4 \sqrt{\frac{\tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)}

         2/t\
1 - 2*sin |-|
          \2/
-------------
     ________
 2*\/ sin(t)

\frac{1 - 2 \sin^{2}{\left(\frac{t}{2} \right)}}{2 \sqrt{\sin{\left(t \right)}}}

           ___ /        2/t\\        
         \/ 2 *|-1 + cot |-||        
               \         \2//        
-------------------------------------
          _____________              
         /       /t\                 
        /     cot|-|                 
       /         \2/    /       2/t\\
4*    /    ----------- *|1 + cot |-||
     /            2/t\  \        \2//
    /      1 + cot |-|               
  \/               \2/

\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{t}{2} \right)} - 1\right)}{4 \sqrt{\frac{\cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)}

            1             
--------------------------
      ________            
     /   1        /pi    \
2*  /  ------ *csc|-- - t|
  \/   csc(t)     \2     /

\frac{1}{2 \sqrt{\frac{1}{\csc{\left(t \right)}}} \csc{\left(- t + \frac{\pi}{2} \right)}}

          2/t   pi\
 1 - 2*cos |- - --|
           \2   2 /
-------------------
      _____________
     /    /    pi\ 
2*  /  cos|t - --| 
  \/      \    2 /

\frac{1 - 2 \cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{\cos{\left(t - \frac{\pi}{2} \right)}}}

             1              
----------------------------
        _____________       
       /      1             
2*    /  ----------- *sec(t)
     /      /    pi\        
    /    sec|t - --|        
  \/        \    2 /

\frac{1}{2 \sqrt{\frac{1}{\sec{\left(t - \frac{\pi}{2} \right)}}} \sec{\left(t \right)}}

1/(2*sqrt(1/sec(t - pi/2))*sec(t))

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¿Cómo vas a descomponer esta cos(t)/(2*sqrt(sin(t))) expresión en fracciones?

Solución