cos(4*l)+sin(2*l)*cos(2*l) если l=-1/4 (упростите выражение)

Выражение, которое надо упростить:

Решение

Вы ввели
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cos(4*l) + sin(2*l)*cos(2*l)
$$\sin{\left (2 l \right )} \cos{\left (2 l \right )} + \cos{\left (4 l \right )}$$
Подстановка условия
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cos(4*l) + sin(2*l)*cos(2*l) при l = -1/4
cos(4*l) + sin(2*l)*cos(2*l)
$$\sin{\left (2 l \right )} \cos{\left (2 l \right )} + \cos{\left (4 l \right )}$$
cos(4*(-1/4)) + sin(2*(-1/4))*cos(2*(-1/4))
$$\sin{\left (2 (-1/4) \right )} \cos{\left (2 (-1/4) \right )} + \cos{\left (4 (-1/4) \right )}$$
cos(4*(-1)/4) + sin(2*(-1)/4)*cos(2*(-1)/4)
$$\sin{\left (\frac{-2}{4} \right )} \cos{\left (\frac{-2}{4} \right )} + \cos{\left (\frac{-4}{4} \right )}$$
-cos(1/2)*sin(1/2) + cos(1)
$$- \sin{\left (\frac{1}{2} \right )} \cos{\left (\frac{1}{2} \right )} + \cos{\left (1 \right )}$$
Численный ответ
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cos(2*l)*sin(2*l) + cos(4*l)
Общее упрощение
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sin(4*l)           
-------- + cos(4*l)
   2               
$$\frac{1}{2} \sin{\left (4 l \right )} + \cos{\left (4 l \right )}$$
Собрать выражение
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sin(4*l)           
-------- + cos(4*l)
   2               
$$\frac{1}{2} \sin{\left (4 l \right )} + \cos{\left (4 l \right )}$$
Тригонометрическая часть
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sin(4*l)           
-------- + cos(4*l)
   2               
$$\frac{1}{2} \sin{\left (4 l \right )} + \cos{\left (4 l \right )}$$
Раскрыть выражение
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   4         4           2       2        /   2         2   \              
cos (l) + sin (l) - 6*cos (l)*sin (l) + 2*\cos (l) - sin (l)/*cos(l)*sin(l)
$$2 \left(- \sin^{2}{\left (l \right )} + \cos^{2}{\left (l \right )}\right) \sin{\left (l \right )} \cos{\left (l \right )} + \sin^{4}{\left (l \right )} - 6 \sin^{2}{\left (l \right )} \cos^{2}{\left (l \right )} + \cos^{4}{\left (l \right )}$$