Общий знаменатель sqrt(1-x^2)*cos(x)/(1+sin ... *atan(sin(x))/sqrt(1-x^2)

Численный ответ

(1.0 - x^2)^0.5*cos(x)/(1.0 + sin(x)^2) - x*(1.0 - x^2)^(-0.5)*atan(sin(x))

Рациональный знаменатель

     ________               ________                      ________               ________                     
    /      2               /      2                  2   /      2               /      2     2                
- \/  1 - x  *cos(x) + x*\/  1 - x  *atan(sin(x)) + x *\/  1 - x  *cos(x) + x*\/  1 - x  *sin (x)*atan(sin(x))
--------------------------------------------------------------------------------------------------------------
                                           /       2   \ /      2\                                            
                                           \1 + sin (x)/*\-1 + x /                                            

$$\frac{1}{\left(x^{2} - 1\right) \left(\sin^{2}{\left (x \right )} + 1\right)} \left(x^{2} \sqrt{- x^{2} + 1} \cos{\left (x \right )} + x \sqrt{- x^{2} + 1} \sin^{2}{\left (x \right )} \operatorname{atan}{\left (\sin{\left (x \right )} \right )} + x \sqrt{- x^{2} + 1} \operatorname{atan}{\left (\sin{\left (x \right )} \right )} - \sqrt{- x^{2} + 1} \cos{\left (x \right )}\right)$$

Объединение рациональных выражений

/     2\            /       2   \             
\1 - x /*cos(x) - x*\1 + sin (x)/*atan(sin(x))
----------------------------------------------
                           ________           
          /       2   \   /      2            
          \1 + sin (x)/*\/  1 - x             

$$\frac{1}{\sqrt{- x^{2} + 1} \left(\sin^{2}{\left (x \right )} + 1\right)} \left(- x \left(\sin^{2}{\left (x \right )} + 1\right) \operatorname{atan}{\left (\sin{\left (x \right )} \right )} + \left(- x^{2} + 1\right) \cos{\left (x \right )}\right)$$

Общее упрощение

/     2\            /       2   \             
\1 - x /*cos(x) - x*\1 + sin (x)/*atan(sin(x))
----------------------------------------------
                           ________           
          /       2   \   /      2            
          \1 + sin (x)/*\/  1 - x             

$$\frac{1}{\sqrt{- x^{2} + 1} \left(\sin^{2}{\left (x \right )} + 1\right)} \left(- x \left(\sin^{2}{\left (x \right )} + 1\right) \operatorname{atan}{\left (\sin{\left (x \right )} \right )} + \left(- x^{2} + 1\right) \cos{\left (x \right )}\right)$$

Собрать выражение

                        ________       
                       /      2        
  x*atan(sin(x))   2*\/  1 - x  *cos(x)
- -------------- - --------------------
      ________        -3 + cos(2*x)    
     /      2                          
   \/  1 - x                           

$$- \frac{x \operatorname{atan}{\left (\sin{\left (x \right )} \right )}}{\sqrt{- x^{2} + 1}} - \frac{2 \sqrt{- x^{2} + 1} \cos{\left (x \right )}}{\cos{\left (2 x \right )} - 3}$$

Комбинаторика

 /                            2               2                \ 
-\-cos(x) + x*atan(sin(x)) + x *cos(x) + x*sin (x)*atan(sin(x))/ 
-----------------------------------------------------------------
                 ___________________ /       2   \               
               \/ -(1 + x)*(-1 + x) *\1 + sin (x)/               

$$- \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(\sin^{2}{\left (x \right )} + 1\right)} \left(x^{2} \cos{\left (x \right )} + x \sin^{2}{\left (x \right )} \operatorname{atan}{\left (\sin{\left (x \right )} \right )} + x \operatorname{atan}{\left (\sin{\left (x \right )} \right )} - \cos{\left (x \right )}\right)$$

Общий знаменатель

 /                            2               2                \ 
-\-cos(x) + x*atan(sin(x)) + x *cos(x) + x*sin (x)*atan(sin(x))/ 
-----------------------------------------------------------------
                   ________      ________                        
                  /      2      /      2     2                   
                \/  1 - x   + \/  1 - x  *sin (x)                

$$- \frac{1}{\sqrt{- x^{2} + 1} \sin^{2}{\left (x \right )} + \sqrt{- x^{2} + 1}} \left(x^{2} \cos{\left (x \right )} + x \sin^{2}{\left (x \right )} \operatorname{atan}{\left (\sin{\left (x \right )} \right )} + x \operatorname{atan}{\left (\sin{\left (x \right )} \right )} - \cos{\left (x \right )}\right)$$