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Общий знаменатель (1+3*x^2-12*x*cos(x)/sin( ... 5+3*x^2)/sin(x)^2)/sin(x)

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
                              2    /        2\
       2   12*x*cos(x)   2*cos (x)*\-5 + 3*x /
1 + 3*x  - ----------- + ---------------------
              sin(x)               2          
                                sin (x)       
----------------------------------------------
                    sin(x)
$$\frac{1}{\sin{\left (x \right )}} \left(\frac{2 \cos^{2}{\left (x \right )}}{\sin^{2}{\left (x \right )}} \left(3 x^{2} - 5\right) + - \frac{12 x \cos{\left (x \right )}}{\sin{\left (x \right )}} + 3 x^{2} + 1\right)$$
Степени [src]
              2    /         2\              
       2   cos (x)*\-10 + 6*x /   12*x*cos(x)
1 + 3*x  + -------------------- - -----------
                    2                sin(x)  
                 sin (x)                     
---------------------------------------------
                    sin(x)
$$\frac{1}{\sin{\left (x \right )}} \left(3 x^{2} - \frac{12 x \cos{\left (x \right )}}{\sin{\left (x \right )}} + \frac{\left(6 x^{2} - 10\right) \cos^{2}{\left (x \right )}}{\sin^{2}{\left (x \right )}} + 1\right)$$
                              2    /        2\
       2   12*x*cos(x)   2*cos (x)*\-5 + 3*x /
1 + 3*x  - ----------- + ---------------------
              sin(x)               2          
                                sin (x)       
----------------------------------------------
                    sin(x)
$$\frac{1}{\sin{\left (x \right )}} \left(3 x^{2} - \frac{12 x \cos{\left (x \right )}}{\sin{\left (x \right )}} + \frac{2 \cos^{2}{\left (x \right )}}{\sin^{2}{\left (x \right )}} \left(3 x^{2} - 5\right) + 1\right)$$
Численный ответ [src]
(1.0 + 3.0*x^2 + 2.0*cos(x)^2*(-5.0 + 3.0*x^2)/sin(x)^2 - 12.0*x*cos(x)/sin(x))/sin(x)
Рациональный знаменатель [src]
   2    //       2\                     \        2    /        2\       
sin (x)*\\1 + 3*x /*sin(x) - 12*x*cos(x)/ + 2*cos (x)*\-5 + 3*x /*sin(x)
------------------------------------------------------------------------
                                   4                                    
                                sin (x)
$$\frac{1}{\sin^{4}{\left (x \right )}} \left(2 \left(3 x^{2} - 5\right) \sin{\left (x \right )} \cos^{2}{\left (x \right )} + \left(- 12 x \cos{\left (x \right )} + \left(3 x^{2} + 1\right) \sin{\left (x \right )}\right) \sin^{2}{\left (x \right )}\right)$$
Объединение рациональных выражений [src]
//       2\                     \               2    /        2\
\\1 + 3*x /*sin(x) - 12*x*cos(x)/*sin(x) + 2*cos (x)*\-5 + 3*x /
----------------------------------------------------------------
                               3                                
                            sin (x)
$$\frac{1}{\sin^{3}{\left (x \right )}} \left(2 \left(3 x^{2} - 5\right) \cos^{2}{\left (x \right )} + \left(- 12 x \cos{\left (x \right )} + \left(3 x^{2} + 1\right) \sin{\left (x \right )}\right) \sin{\left (x \right )}\right)$$
Общее упрощение [src]
   2    /         2\      2    /       2\               
cos (x)*\-10 + 6*x / + sin (x)*\1 + 3*x / - 6*x*sin(2*x)
--------------------------------------------------------
                           3                            
                        sin (x)
$$\frac{1}{\sin^{3}{\left (x \right )}} \left(- 6 x \sin{\left (2 x \right )} + \left(3 x^{2} + 1\right) \sin^{2}{\left (x \right )} + \left(6 x^{2} - 10\right) \cos^{2}{\left (x \right )}\right)$$
Собрать выражение [src]
                2    /        2\              
       2   2*cos (x)*\-5 + 3*x /   12*x*cos(x)
1 + 3*x  + --------------------- - -----------
                     2                sin(x)  
                  sin (x)                     
----------------------------------------------
                    sin(x)
$$\frac{1}{\sin{\left (x \right )}} \left(3 x^{2} - \frac{12 x \cos{\left (x \right )}}{\sin{\left (x \right )}} + \frac{2 \cos^{2}{\left (x \right )}}{\sin^{2}{\left (x \right )}} \left(3 x^{2} - 5\right) + 1\right)$$
/          2         2                    2    2   \       
\1 - 10*cot (x) + 3*x  - 12*x*cot(x) + 6*x *cot (x)/*csc(x)
$$\left(6 x^{2} \cot^{2}{\left (x \right )} + 3 x^{2} - 12 x \cot{\left (x \right )} - 10 \cot^{2}{\left (x \right )} + 1\right) \csc{\left (x \right )}$$
Общий знаменатель [src]
   2            2         2    2         2    2                        
sin (x) - 10*cos (x) + 3*x *sin (x) + 6*x *cos (x) - 12*x*cos(x)*sin(x)
-----------------------------------------------------------------------
                                   3                                   
                                sin (x)
$$\frac{1}{\sin^{3}{\left (x \right )}} \left(3 x^{2} \sin^{2}{\left (x \right )} + 6 x^{2} \cos^{2}{\left (x \right )} - 12 x \sin{\left (x \right )} \cos{\left (x \right )} + \sin^{2}{\left (x \right )} - 10 \cos^{2}{\left (x \right )}\right)$$
Тригонометрическая часть [src]
                    2         
       2   -10 + 6*x     12*x 
1 + 3*x  + ---------- - ------
               2        tan(x)
            tan (x)           
------------------------------
            sin(x)
$$\frac{1}{\sin{\left (x \right )}} \left(3 x^{2} - \frac{12 x}{\tan{\left (x \right )}} + \frac{6 x^{2} - 10}{\tan^{2}{\left (x \right )}} + 1\right)$$
Комбинаторика [src]
   2            2         2    2         2    2                        
sin (x) - 10*cos (x) + 3*x *sin (x) + 6*x *cos (x) - 12*x*cos(x)*sin(x)
-----------------------------------------------------------------------
                                   3                                   
                                sin (x)
$$\frac{1}{\sin^{3}{\left (x \right )}} \left(3 x^{2} \sin^{2}{\left (x \right )} + 6 x^{2} \cos^{2}{\left (x \right )} - 12 x \sin{\left (x \right )} \cos{\left (x \right )} + \sin^{2}{\left (x \right )} - 10 \cos^{2}{\left (x \right )}\right)$$
Раскрыть выражение [src]
              2    /         2\              
       2   cos (x)*\-10 + 6*x /   12*x*cos(x)
1 + 3*x  + -------------------- - -----------
                    2                sin(x)  
                 sin (x)                     
---------------------------------------------
                    sin(x)
$$\frac{1}{\sin{\left (x \right )}} \left(3 x^{2} - \frac{12 x \cos{\left (x \right )}}{\sin{\left (x \right )}} + \frac{\left(6 x^{2} - 10\right) \cos^{2}{\left (x \right )}}{\sin^{2}{\left (x \right )}} + 1\right)$$