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Общий знаменатель (2^(3/2)*sin(x))/((1+cos( ... sin(x)^2/(1+cos(x))^2+1))

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
              3/2                     
             2   *sin(x)              
--------------------------------------
                   ___________________
                  /       2           
                 /     sin (x)        
(1 + cos(x))*   /   ------------- + 1 
               /                2     
             \/     (1 + cos(x))
232sin⁡(x)1+sin⁡2(x)(cos⁡(x)+1)2(cos⁡(x)+1)\frac{2^{\frac{3}{2}} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right)^{2}}} \left(\cos{\left (x \right )} + 1\right)}
Степени [src]
                ___                   
            2*\/ 2 *sin(x)            
--------------------------------------
      ___________________             
     /           2                    
    /         sin (x)                 
   /   1 + ------------- *(1 + cos(x))
  /                    2              
\/         (1 + cos(x))
22sin⁡(x)1+sin⁡2(x)(cos⁡(x)+1)2(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right)^{2}}} \left(\cos{\left (x \right )} + 1\right)}
Численный ответ [src]
2.82842712474619*(1.0 + sin(x)^2/(1.0 + cos(x))^2)^(-0.5)*sin(x)/(1.0 + cos(x))
Рациональный знаменатель [src]
                     ___                       
                 2*\/ 2 *sin(x)                
-----------------------------------------------
      ____________________________             
     /               2                         
    /             sin (x)                      
   /   1 + ---------------------- *(1 + cos(x))
  /               2                            
\/         1 + cos (x) + 2*cos(x)
22sin⁡(x)1+sin⁡2(x)cos⁡2(x)+2cos⁡(x)+1(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )} + 2 \cos{\left (x \right )} + 1}} \left(\cos{\left (x \right )} + 1\right)}
Объединение рациональных выражений [src]
                   ___                      
               2*\/ 2 *sin(x)               
--------------------------------------------
      _________________________             
     /             2      2                 
    /  (1 + cos(x))  + sin (x)              
   /   ----------------------- *(1 + cos(x))
  /                     2                   
\/          (1 + cos(x))
22sin⁡(x)(cos⁡(x)+1)2+sin⁡2(x)(cos⁡(x)+1)2(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{\frac{\left(\cos{\left (x \right )} + 1\right)^{2} + \sin^{2}{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right)^{2}}} \left(\cos{\left (x \right )} + 1\right)}
Общее упрощение [src]
           2*sin(x)          
-----------------------------
    ____________             
   /     1                   
  /  ---------- *(1 + cos(x))
\/   1 + cos(x)
2sin⁡(x)(cos⁡(x)+1)1cos⁡(x)+1\frac{2 \sin{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right) \sqrt{\frac{1}{\cos{\left (x \right )} + 1}}}
Собрать выражение [src]
                ___                   
            2*\/ 2 *sin(x)            
--------------------------------------
      ___________________             
     /           2                    
    /         sin (x)                 
   /   1 + ------------- *(1 + cos(x))
  /                    2              
\/         (1 + cos(x))
22sin⁡(x)1+sin⁡2(x)(cos⁡(x)+1)2(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right)^{2}}} \left(\cos{\left (x \right )} + 1\right)}
    ___   _________________________       
2*\/ 2 *\/ 3 + 4*cos(x) + cos(2*x) *sin(x)
------------------------------------------
  ______________     ______________       
\/ 4 + 4*cos(x)  + \/ 4 + 4*cos(x) *cos(x)
224cos⁡(x)+cos⁡(2x)+3sin⁡(x)4cos⁡(x)+4cos⁡(x)+4cos⁡(x)+4\frac{2 \sqrt{2} \sqrt{4 \cos{\left (x \right )} + \cos{\left (2 x \right )} + 3} \sin{\left (x \right )}}{\sqrt{4 \cos{\left (x \right )} + 4} \cos{\left (x \right )} + \sqrt{4 \cos{\left (x \right )} + 4}}
Комбинаторика [src]
                        ___                          
                    2*\/ 2 *sin(x)                   
-----------------------------------------------------
      __________________________________             
     /        2         2                            
    /  1 + cos (x) + sin (x) + 2*cos(x)              
   /   -------------------------------- *(1 + cos(x))
  /                2                                 
\/          1 + cos (x) + 2*cos(x)
22sin⁡(x)sin⁡2(x)+cos⁡2(x)+2cos⁡(x)+1cos⁡2(x)+2cos⁡(x)+1(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{\frac{\sin^{2}{\left (x \right )} + \cos^{2}{\left (x \right )} + 2 \cos{\left (x \right )} + 1}{\cos^{2}{\left (x \right )} + 2 \cos{\left (x \right )} + 1}} \left(\cos{\left (x \right )} + 1\right)}
Общий знаменатель [src]
                                    ___                                       
                                2*\/ 2 *sin(x)                                
------------------------------------------------------------------------------
      ____________________________         ____________________________       
     /               2                    /               2                   
    /             sin (x)                /             sin (x)                
   /   1 + ----------------------  +    /   1 + ---------------------- *cos(x)
  /               2                    /               2                      
\/         1 + cos (x) + 2*cos(x)    \/         1 + cos (x) + 2*cos(x)
22sin⁡(x)1+sin⁡2(x)cos⁡2(x)+2cos⁡(x)+1cos⁡(x)+1+sin⁡2(x)cos⁡2(x)+2cos⁡(x)+1\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )} + 2 \cos{\left (x \right )} + 1}} \cos{\left (x \right )} + \sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )} + 2 \cos{\left (x \right )} + 1}}}
Тригонометрическая часть [src]
           2*sin(x)          
-----------------------------
    ____________             
   /     1                   
  /  ---------- *(1 + cos(x))
\/   1 + cos(x)
2sin⁡(x)(cos⁡(x)+1)1cos⁡(x)+1\frac{2 \sin{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right) \sqrt{\frac{1}{\cos{\left (x \right )} + 1}}}
Раскрыть выражение [src]
                ___                   
            2*\/ 2 *sin(x)            
--------------------------------------
      ___________________             
     /           2                    
    /         sin (x)                 
   /   1 + ------------- *(1 + cos(x))
  /                    2              
\/         (1 + cos(x))
22sin⁡(x)1+sin⁡2(x)(cos⁡(x)+1)2(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right)^{2}}} \left(\cos{\left (x \right )} + 1\right)}
                ___                   
            2*\/ 2 *sin(x)            
--------------------------------------
                   ___________________
                  /       2           
                 /     sin (x)        
(1 + cos(x))*   /   ------------- + 1 
               /                2     
             \/     (1 + cos(x))
22sin⁡(x)1+sin⁡2(x)(cos⁡(x)+1)2(cos⁡(x)+1)\frac{2 \sqrt{2} \sin{\left (x \right )}}{\sqrt{1 + \frac{\sin^{2}{\left (x \right )}}{\left(\cos{\left (x \right )} + 1\right)^{2}}} \left(\cos{\left (x \right )} + 1\right)}