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Общий знаменатель sin(x)/(((1-tan(x/2))/(1+tan(x/2)))*(1+sin(x)))

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Примеры

Решение

Вы ввели [src]
         sin(x)        
-----------------------
       /x\             
1 - tan|-|             
       \2/             
----------*(1 + sin(x))
       /x\             
1 + tan|-|             
       \2/
$$\frac{\sin{\left (x \right )}}{\frac{- \tan{\left (\frac{x}{2} \right )} + 1}{\tan{\left (\frac{x}{2} \right )} + 1} \left(\sin{\left (x \right )} + 1\right)}$$
Степени [src]
   /       /x\\          
   |1 + tan|-||*sin(x)   
   \       \2//          
-------------------------
/       /x\\             
|1 - tan|-||*(1 + sin(x))
\       \2//
$$\frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(- \tan{\left (\frac{x}{2} \right )} + 1\right)}$$
Численный ответ [src]
(1.0 + tan(x/2))*sin(x)/((1.0 - tan(x/2))*(1.0 + sin(x)))
Рациональный знаменатель [src]
   /       /x\\          
   |1 + tan|-||*sin(x)   
   \       \2//          
-------------------------
/       /x\\             
|1 - tan|-||*(1 + sin(x))
\       \2//
$$\frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(- \tan{\left (\frac{x}{2} \right )} + 1\right)}$$
Объединение рациональных выражений [src]
   /       /x\\          
   |1 + tan|-||*sin(x)   
   \       \2//          
-------------------------
/       /x\\             
|1 - tan|-||*(1 + sin(x))
\       \2//
$$\frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(- \tan{\left (\frac{x}{2} \right )} + 1\right)}$$
Общее упрощение [src]
   /       /x\\           
  -|1 + tan|-||*sin(x)    
   \       \2//           
--------------------------
             /        /x\\
(1 + sin(x))*|-1 + tan|-||
             \        \2//
$$- \frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(\tan{\left (\frac{x}{2} \right )} - 1\right)}$$
Собрать выражение [src]
   /       /x\\          
   |1 + tan|-||*sin(x)   
   \       \2//          
-------------------------
/       /x\\             
|1 - tan|-||*(1 + sin(x))
\       \2//
$$\frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(- \tan{\left (\frac{x}{2} \right )} + 1\right)}$$
                                                              /x\            
                                                    sin(x)*tan|-|            
                 sin(x)                                       \2/            
- ------------------------------------ - ------------------------------------
                          /x\      /x\                           /x\      /x\
  -1 - sin(x) + sin(x)*tan|-| + tan|-|   -1 - sin(x) + sin(x)*tan|-| + tan|-|
                          \2/      \2/                           \2/      \2/
$$- \frac{\sin{\left (x \right )} \tan{\left (\frac{x}{2} \right )}}{\sin{\left (x \right )} \tan{\left (\frac{x}{2} \right )} - \sin{\left (x \right )} + \tan{\left (\frac{x}{2} \right )} - 1} - \frac{\sin{\left (x \right )}}{\sin{\left (x \right )} \tan{\left (\frac{x}{2} \right )} - \sin{\left (x \right )} + \tan{\left (\frac{x}{2} \right )} - 1}$$
Комбинаторика [src]
   /       /x\\           
  -|1 + tan|-||*sin(x)    
   \       \2//           
--------------------------
             /        /x\\
(1 + sin(x))*|-1 + tan|-||
             \        \2//
$$- \frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(\tan{\left (\frac{x}{2} \right )} - 1\right)}$$
Общий знаменатель [src]
                   /x\                   
            1 - tan|-| + 2*sin(x)        
                   \2/                   
-1 - ------------------------------------
                             /x\      /x\
     -1 - sin(x) + sin(x)*tan|-| + tan|-|
                             \2/      \2/
$$- \frac{2 \sin{\left (x \right )} - \tan{\left (\frac{x}{2} \right )} + 1}{\sin{\left (x \right )} \tan{\left (\frac{x}{2} \right )} - \sin{\left (x \right )} + \tan{\left (\frac{x}{2} \right )} - 1} - 1$$
Тригонометрическая часть [src]
   /       /x\\          
   |1 + tan|-||*sin(x)   
   \       \2//          
-------------------------
/       /x\\             
|1 - tan|-||*(1 + sin(x))
\       \2//
$$\frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(- \tan{\left (\frac{x}{2} \right )} + 1\right)}$$
Раскрыть выражение [src]
   /       /x\\          
   |1 + tan|-||*sin(x)   
   \       \2//          
-------------------------
/       /x\\             
|1 - tan|-||*(1 + sin(x))
\       \2//
$$\frac{\left(\tan{\left (\frac{x}{2} \right )} + 1\right) \sin{\left (x \right )}}{\left(\sin{\left (x \right )} + 1\right) \left(- \tan{\left (\frac{x}{2} \right )} + 1\right)}$$