-2*cos(2*x)*sin(cos(2*x)) ... n(2*x))*sin(2*x) если x=4 (упростите выражение)

Вы ввели

-2*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

$$\sin{\left (\cos{\left (2 x \right )} \right )} \left(- 2 \cos{\left (2 x \right )}\right) \sin{\left (\sin{\left (2 x \right )} \right )} - 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )}$$

Подстановка условия

((-2*cos(2*x))*sin(cos(2*x)))*sin(sin(2*x)) - (2*cos(cos(2*x)))*cos(sin(2*x))*sin(2*x) при x = 4

((-2*cos(2*x))*sin(cos(2*x)))*sin(sin(2*x)) - (2*cos(cos(2*x)))*cos(sin(2*x))*sin(2*x)

$$\sin{\left (\cos{\left (2 x \right )} \right )} \left(- 2 \cos{\left (2 x \right )}\right) \sin{\left (\sin{\left (2 x \right )} \right )} - 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )}$$

((-2*cos(2*(4)))*sin(cos(2*(4))))*sin(sin(2*(4))) - (2*cos(cos(2*(4))))*cos(sin(2*(4)))*sin(2*(4))

$$\sin{\left (\cos{\left (2 (4) \right )} \right )} \left(- 2 \cos{\left (2 (4) \right )}\right) \sin{\left (\sin{\left (2 (4) \right )} \right )} - 2 \sin{\left (2 (4) \right )} \cos{\left (\sin{\left (2 (4) \right )} \right )} \cos{\left (\cos{\left (2 (4) \right )} \right )}$$

((-2*cos(2*4))*sin(cos(2*4)))*sin(sin(2*4)) - (2*cos(cos(2*4)))*cos(sin(2*4))*sin(2*4)

$$- 2 \sin{\left (2 \cdot 4 \right )} \cos{\left (\sin{\left (2 \cdot 4 \right )} \right )} \cos{\left (\cos{\left (2 \cdot 4 \right )} \right )} + \sin{\left (\cos{\left (2 \cdot 4 \right )} \right )} \left(- 2 \cos{\left (2 \cdot 4 \right )}\right) \sin{\left (\sin{\left (2 \cdot 4 \right )} \right )}$$

-2*cos(8)*sin(cos(8))*sin(sin(8)) - 2*cos(cos(8))*cos(sin(8))*sin(8)

$$- 2 \sin{\left (8 \right )} \cos{\left (\sin{\left (8 \right )} \right )} \cos{\left (\cos{\left (8 \right )} \right )} - 2 \sin{\left (\sin{\left (8 \right )} \right )} \sin{\left (\cos{\left (8 \right )} \right )} \cos{\left (8 \right )}$$

Степени

-2*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

$$- 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} - 2 \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}$$

Численный ответ

-2.0*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2.0*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

Рациональный знаменатель

-2*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

$$- 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} - 2 \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}$$

Объединение рациональных выражений

2*(-cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - cos(cos(2*x))*cos(sin(2*x))*sin(2*x))

$$2 \left(- \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} - \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}\right)$$

Общее упрощение

-2*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

$$- 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} - 2 \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}$$

Собрать выражение

cos(-2*x + cos(2*x) + sin(2*x))   cos(2*x + cos(2*x) + sin(2*x))   sin(-2*x + cos(2*x) + sin(2*x))   cos(-cos(2*x) + 2*x + sin(2*x))   cos(-sin(2*x) + 2*x + cos(2*x))   sin(-cos(2*x) + 2*x + sin(2*x))   sin(-sin(2*x) + 2*x + cos(2*x))   sin(2*x + cos(2*x) + sin(2*x))
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$$\frac{1}{2} \sin{\left (- 2 x + \sin{\left (2 x \right )} + \cos{\left (2 x \right )} \right )} - \frac{1}{2} \sin{\left (2 x - \sin{\left (2 x \right )} + \cos{\left (2 x \right )} \right )} - \frac{1}{2} \sin{\left (2 x + \sin{\left (2 x \right )} - \cos{\left (2 x \right )} \right )} - \frac{1}{2} \sin{\left (2 x + \sin{\left (2 x \right )} + \cos{\left (2 x \right )} \right )} + \frac{1}{2} \cos{\left (- 2 x + \sin{\left (2 x \right )} + \cos{\left (2 x \right )} \right )} - \frac{1}{2} \cos{\left (2 x - \sin{\left (2 x \right )} + \cos{\left (2 x \right )} \right )} - \frac{1}{2} \cos{\left (2 x + \sin{\left (2 x \right )} - \cos{\left (2 x \right )} \right )} + \frac{1}{2} \cos{\left (2 x + \sin{\left (2 x \right )} + \cos{\left (2 x \right )} \right )}$$

Комбинаторика

-2*(cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) + cos(cos(2*x))*cos(sin(2*x))*sin(2*x))

$$- 2 \left(\sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} + \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}\right)$$

Общий знаменатель

-2*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

$$- 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} - 2 \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}$$

Тригонометрическая часть

-2*cos(2*x)*sin(cos(2*x))*sin(sin(2*x)) - 2*cos(cos(2*x))*cos(sin(2*x))*sin(2*x)

$$- 2 \sin{\left (2 x \right )} \cos{\left (\sin{\left (2 x \right )} \right )} \cos{\left (\cos{\left (2 x \right )} \right )} - 2 \sin{\left (\sin{\left (2 x \right )} \right )} \sin{\left (\cos{\left (2 x \right )} \right )} \cos{\left (2 x \right )}$$

Раскрыть выражение

/       2           2   \                         /   2         2   \                                    /   2         2   \       
\- 2*sin (x) + 2*cos (x)/*sin(2*cos(x)*sin(x))*sin\sin (x) - cos (x)/ - 4*cos(x)*cos(2*cos(x)*sin(x))*cos\sin (x) - cos (x)/*sin(x)

$$\left(- 2 \sin^{2}{\left (x \right )} + 2 \cos^{2}{\left (x \right )}\right) \sin{\left (2 \sin{\left (x \right )} \cos{\left (x \right )} \right )} \sin{\left (\sin^{2}{\left (x \right )} - \cos^{2}{\left (x \right )} \right )} - 4 \sin{\left (x \right )} \cos{\left (x \right )} \cos{\left (2 \sin{\left (x \right )} \cos{\left (x \right )} \right )} \cos{\left (\sin^{2}{\left (x \right )} - \cos^{2}{\left (x \right )} \right )}$$