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

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
    /   2       \                               
-log\sin (x) - 1/                        1      
------------------ + log(sin(x)) - -------------
        2                               2       
                                   2*sin (x) - 2
$$\frac{1}{2} \left(-1 \log{\left (\sin^{2}{\left (x \right )} - 1 \right )}\right) + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )} - 2}$$
Степени [src]
                      /        2   \              
        1          log\-1 + sin (x)/              
- -------------- - ----------------- + log(sin(x))
            2              2                      
  -2 + 2*sin (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )} - 2}$$
Численный ответ [src]
-1/(-2.0 + 2.0*sin(x)^2) - 0.5*log(sin(x)^2 - 1) + log(sin(x))
Рациональный знаменатель [src]
                        2       /        2   \        2                     /        2   \
-1 - 2*log(sin(x)) - sin (x)*log\-1 + sin (x)/ + 2*sin (x)*log(sin(x)) + log\-1 + sin (x)/
------------------------------------------------------------------------------------------
                                                2                                         
                                      -2 + 2*sin (x)
$$\frac{1}{2 \sin^{2}{\left (x \right )} - 2} \left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} \sin^{2}{\left (x \right )} + \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + 2 \log{\left (\sin{\left (x \right )} \right )} \sin^{2}{\left (x \right )} - 2 \log{\left (\sin{\left (x \right )} \right )} - 1\right)$$
Объединение рациональных выражений [src]
     /        2   \ /     /        2   \                \
-1 + \-1 + sin (x)/*\- log\-1 + sin (x)/ + 2*log(sin(x))/
---------------------------------------------------------
                       /        2   \                    
                     2*\-1 + sin (x)/
$$\frac{1}{2 \sin^{2}{\left (x \right )} - 2} \left(\left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + 2 \log{\left (\sin{\left (x \right )} \right )}\right) \left(\sin^{2}{\left (x \right )} - 1\right) - 1\right)$$
Общее упрощение [src]
               /        2   \              
    1       log\-1 + sin (x)/              
--------- - ----------------- + log(sin(x))
     2              2                      
2*cos (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} + \frac{1}{2 \cos^{2}{\left (x \right )}}$$
Общий знаменатель [src]
                      /        2   \              
        1          log\-1 + sin (x)/              
- -------------- - ----------------- + log(sin(x))
            2              2                      
  -2 + 2*sin (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )} - 2}$$
Тригонометрическая часть [src]
               /    2   \              
    1       log\-cos (x)/              
--------- - ------------- + log(sin(x))
     2            2                    
2*cos (x)
$$\log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \log{\left (- \cos^{2}{\left (x \right )} \right )} + \frac{1}{2 \cos^{2}{\left (x \right )}}$$
Комбинаторика [src]
                        2       /        2   \        2                     /        2   \
-1 - 2*log(sin(x)) - sin (x)*log\-1 + sin (x)/ + 2*sin (x)*log(sin(x)) + log\-1 + sin (x)/
------------------------------------------------------------------------------------------
                               2*(1 + sin(x))*(-1 + sin(x))
$$\frac{1}{2 \left(\sin{\left (x \right )} - 1\right) \left(\sin{\left (x \right )} + 1\right)} \left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} \sin^{2}{\left (x \right )} + \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + 2 \log{\left (\sin{\left (x \right )} \right )} \sin^{2}{\left (x \right )} - 2 \log{\left (\sin{\left (x \right )} \right )} - 1\right)$$
Раскрыть выражение [src]
                      /        2   \              
        1          log\-1 + sin (x)/              
- -------------- - ----------------- + log(sin(x))
            2              2                      
  -2 + 2*sin (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )} - 2}$$