(sin(8*a)+sin(2*a))*1/((cos(8*a)+cos(2*a)*cot(5)*a)^1) если a=2 (упростите выражение)

Выражение, которое надо упростить:

Решение

Вы ввели
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      sin(8*a) + sin(2*a)      
-------------------------------
                              1
(cos(8*a) + cos(2*a)*cot(5)*a) 
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{\left(a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}\right)^{1}}$$
Подстановка условия
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(sin(8*a) + sin(2*a))/(cos(8*a) + (cos(2*a)*cot(5))*a)^1 при a = 2
(sin(8*a) + sin(2*a))/(cos(8*a) + (cos(2*a)*cot(5))*a)^1
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{\left(a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}\right)^{1}}$$
(sin(8*(2)) + sin(2*(2)))/(cos(8*(2)) + (cos(2*(2))*cot(5))*(2))^1
$$\frac{\sin{\left (2 (2) \right )} + \sin{\left (8 (2) \right )}}{\left((2) \cos{\left (2 (2) \right )} \cot{\left (5 \right )} + \cos{\left (8 (2) \right )}\right)^{1}}$$
(sin(8*2) + sin(2*2))/(cos(8*2) + (cos(2*2)*cot(5))*2)^1
$$\frac{\sin{\left (2 \cdot 2 \right )} + \sin{\left (2 \cdot 8 \right )}}{\left(\cos{\left (2 \cdot 8 \right )} + 2 \cos{\left (2 \cdot 2 \right )} \cot{\left (5 \right )}\right)^{1}}$$
(sin(4) + sin(16))/(2*cos(4)*cot(5) + cos(16))
$$\frac{\sin{\left (4 \right )} + \sin{\left (16 \right )}}{\cos{\left (16 \right )} + 2 \cos{\left (4 \right )} \cot{\left (5 \right )}}$$
Степени
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    sin(2*a) + sin(8*a)     
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a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Численный ответ
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(sin(2*a) + sin(8*a))/(-0.295812915532746*a*cos(2*a) + cos(8*a))
Рациональный знаменатель
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    sin(2*a) + sin(8*a)     
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a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Объединение рациональных выражений
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    sin(2*a) + sin(8*a)     
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a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Общее упрощение
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    sin(2*a) + sin(8*a)     
----------------------------
a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Собрать выражение
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    sin(2*a) + sin(8*a)     
----------------------------
cos(2*a)*cot(5)*a + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
          sin(2*a)                       sin(8*a)          
---------------------------- + ----------------------------
a*cos(2*a)*cot(5) + cos(8*a)   a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}} + \frac{\sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Комбинаторика
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    sin(2*a) + sin(8*a)     
----------------------------
a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Общий знаменатель
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    sin(2*a) + sin(8*a)     
----------------------------
a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Тригонометрическая часть
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    sin(8*a) + sin(2*a)     
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a*cos(2*a)*cot(5) + cos(8*a)
$$\frac{\sin{\left (2 a \right )} + \sin{\left (8 a \right )}}{a \cos{\left (2 a \right )} \cot{\left (5 \right )} + \cos{\left (8 a \right )}}$$
Раскрыть выражение
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               5       3           7                                    7                   3       5          
       - 56*cos (a)*sin (a) - 8*sin (a)*cos(a) + 2*cos(a)*sin(a) + 8*cos (a)*sin(a) + 56*cos (a)*sin (a)       
---------------------------------------------------------------------------------------------------------------
   8         8            2       6            6       2            4       4        /   2         2   \       
cos (a) + sin (a) - 28*cos (a)*sin (a) - 28*cos (a)*sin (a) + 70*cos (a)*sin (a) + a*\cos (a) - sin (a)/*cot(5)
$$\frac{- 8 \sin^{7}{\left (a \right )} \cos{\left (a \right )} + 56 \sin^{5}{\left (a \right )} \cos^{3}{\left (a \right )} - 56 \sin^{3}{\left (a \right )} \cos^{5}{\left (a \right )} + 8 \sin{\left (a \right )} \cos^{7}{\left (a \right )} + 2 \sin{\left (a \right )} \cos{\left (a \right )}}{a \left(- \sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}\right) \cot{\left (5 \right )} + \sin^{8}{\left (a \right )} - 28 \sin^{6}{\left (a \right )} \cos^{2}{\left (a \right )} + 70 \sin^{4}{\left (a \right )} \cos^{4}{\left (a \right )} - 28 \sin^{2}{\left (a \right )} \cos^{6}{\left (a \right )} + \cos^{8}{\left (a \right )}}$$