Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)/(2*sqrt(1+sin(x)))

¿Cómo vas a descomponer esta cos(x)/(2*sqrt(1+sin(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     cos(x)     
----------------
    ____________
2*\/ 1 + sin(x)
cos⁡(x)2sin⁡(x)+1\frac{\cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} 
cos(x)/((2*sqrt(1 + sin(x))))
Respuesta numérica [src] 
0.5*(1.0 + sin(x))^(-0.5)*cos(x)
0.5*(1.0 + sin(x))^(-0.5)*cos(x)
Potencias [src] 
           I*x    -I*x         
          e      e             
          ---- + -----         
           2       2           
-------------------------------
       ________________________
      /       /   -I*x    I*x\ 
     /      I*\- e     + e   / 
2*  /   1 - ------------------ 
  \/                2
eix2+e−ix22−i(eix−e−ix)2+1\frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{2 \sqrt{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1}} 
(exp(i*x)/2 + exp(-i*x)/2)/(2*sqrt(1 - i*(-exp(-i*x) + exp(i*x))/2))
Denominador racional [src] 
  ____________       
\/ 1 + sin(x) *cos(x)
---------------------
     2 + 2*sin(x)
sin⁡(x)+1cos⁡(x)2sin⁡(x)+2\frac{\sqrt{\sin{\left(x \right)} + 1} \cos{\left(x \right)}}{2 \sin{\left(x \right)} + 2} 
sqrt(1 + sin(x))*cos(x)/(2 + 2*sin(x))
Parte trigonométrica [src] 
                2/x\       
           8*cot |-|       
                 \4/       
     1 - --------------    
                      2    
         /       2/x\\     
         |1 + cot |-||     
         \        \4//     
---------------------------
          _________________
         /            /x\  
        /        2*cot|-|  
       /              \2/  
2*    /    1 + ----------- 
     /                2/x\ 
    /          1 + cot |-| 
  \/                   \2/
1−8cot⁡2(x4)(cot⁡2(x4)+1)221+2cot⁡(x2)cot⁡2(x2)+1\frac{1 - \frac{8 \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}}{2 \sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}} 
              2          
     1 - ------------    
            2/x   pi\    
         sec |- - --|    
             \2   2 /    
-------------------------
        _________________
       /          1      
2*    /  1 + ----------- 
     /          /    pi\ 
    /        sec|x - --| 
  \/            \    2 /
1−2sec⁡2(x2−π2)21+1sec⁡(x−π2)\frac{1 - \frac{2}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}}{2 \sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}}} 
            1            
-------------------------
      ____________       
     /       1           
2*  /  1 + ------ *sec(x)
  \/       csc(x)
121+1csc⁡(x)sec⁡(x)\frac{1}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \sec{\left(x \right)}} 
               1                
--------------------------------
        _________________       
       /          1             
2*    /  1 + ----------- *sec(x)
     /          /    pi\        
    /        sec|x - --|        
  \/            \    2 /
121+1sec⁡(x−π2)sec⁡(x)\frac{1}{2 \sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}} 
                      2/x\               
               1 - tan |-|               
                       \2/               
-----------------------------------------
                        _________________
                       /            /x\  
                      /        2*tan|-|  
  /       2/x\\      /              \2/  
2*|1 + tan |-||*    /    1 + ----------- 
  \        \2//    /                2/x\ 
                  /          1 + tan |-| 
                \/                   \2/
1−tan⁡2(x2)21+2tan⁡(x2)tan⁡2(x2)+1(tan⁡2(x2)+1)\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
                       2/x\              
               -1 + cot |-|              
                        \2/              
-----------------------------------------
                        _________________
                       /            /x\  
                      /        2*cot|-|  
  /       2/x\\      /              \2/  
2*|1 + cot |-||*    /    1 + ----------- 
  \        \2//    /                2/x\ 
                  /          1 + cot |-| 
                \/                   \2/
cot⁡2(x2)−121+2cot⁡(x2)cot⁡2(x2)+1(cot⁡2(x2)+1)\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{2 \sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
            2/x   pi\  
   1 - 2*cos |- - --|  
             \2   2 /  
-----------------------
      _________________
     /        /    pi\ 
2*  /  1 + cos|x - --| 
  \/          \    2 /
1−2cos⁡2(x2−π2)2cos⁡(x−π2)+1\frac{1 - 2 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}} 
              1               
------------------------------
      ____________            
     /       1        /pi    \
2*  /  1 + ------ *csc|-- - x|
  \/       csc(x)     \2     /
121+1csc⁡(x)csc⁡(−x+π2)\frac{1}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}} 
     /    pi\   
  sin|x + --|   
     \    2 /   
----------------
    ____________
2*\/ 1 + sin(x)
sin⁡(x+π2)2sin⁡(x)+1\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} 
          2       
   1 - -------    
          2/x\    
       csc |-|    
           \2/    
------------------
      ____________
     /       1    
2*  /  1 + ------ 
  \/       csc(x)
1−2csc⁡2(x2)21+1csc⁡(x)\frac{1 - \frac{2}{\csc^{2}{\left(\frac{x}{2} \right)}}}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}}} 
         cos(x)        
-----------------------
      _________________
     /        /    pi\ 
2*  /  1 + cos|x - --| 
  \/          \    2 /
cos⁡(x)2cos⁡(x−π2)+1\frac{\cos{\left(x \right)}}{2 \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}} 
          2/x\  
 1 - 2*sin |-|  
           \2/  
----------------
    ____________
2*\/ 1 + sin(x)
1−2sin⁡2(x2)2sin⁡(x)+1\frac{1 - 2 \sin^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} 
                2/x\       
           8*tan |-|       
                 \4/       
     1 - --------------    
                      2    
         /       2/x\\     
         |1 + tan |-||     
         \        \4//     
---------------------------
          _________________
         /            /x\  
        /        2*tan|-|  
       /              \2/  
2*    /    1 + ----------- 
     /                2/x\ 
    /          1 + tan |-| 
  \/                   \2/
1−8tan⁡2(x4)(tan⁡2(x4)+1)221+2tan⁡(x2)tan⁡2(x2)+1\frac{1 - \frac{8 \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}}{2 \sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}} 
(1 - 8*tan(x/4)^2/(1 + tan(x/4)^2)^2)/(2*sqrt(1 + 2*tan(x/2)/(1 + tan(x/2)^2)))
    © Sr Examen – Калькулятор