(tan(x)+cot(x))*sin(2*x) если x=-3/2 (упростите выражение)

Выражение, которое надо упростить:

Решение

Вы ввели
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(tan(x) + cot(x))*sin(2*x)
$$\left(\tan{\left (x \right )} + \cot{\left (x \right )}\right) \sin{\left (2 x \right )}$$
Подстановка условия
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(tan(x) + cot(x))*sin(2*x) при x = -3/2
(tan(x) + cot(x))*sin(2*x)
$$\left(\tan{\left (x \right )} + \cot{\left (x \right )}\right) \sin{\left (2 x \right )}$$
(tan((-3/2)) + cot((-3/2)))*sin(2*(-3/2))
$$\left(\tan{\left ((-3/2) \right )} + \cot{\left ((-3/2) \right )}\right) \sin{\left (2 (-3/2) \right )}$$
(tan(-3/2) + cot(-3/2))*sin(2*(-3)/2)
$$\left(\tan{\left (- \frac{3}{2} \right )} + \cot{\left (- \frac{3}{2} \right )}\right) \sin{\left (\frac{-6}{2} \right )}$$
-(-cot(3/2) - tan(3/2))*sin(3)
$$-1 \left(-1 \tan{\left (\frac{3}{2} \right )} + -1 \cot{\left (\frac{3}{2} \right )}\right) \sin{\left (3 \right )}$$
Численный ответ
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(cot(x) + tan(x))*sin(2*x)
Собрать выражение
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cot(x)*sin(2*x) + sin(2*x)*tan(x)
$$\sin{\left (2 x \right )} \tan{\left (x \right )} + \sin{\left (2 x \right )} \cot{\left (x \right )}$$
Общий знаменатель
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cot(x)*sin(2*x) + sin(2*x)*tan(x)
$$\sin{\left (2 x \right )} \tan{\left (x \right )} + \sin{\left (2 x \right )} \cot{\left (x \right )}$$
Раскрыть выражение
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2*(cot(x) + tan(x))*cos(x)*sin(x)
$$2 \left(\tan{\left (x \right )} + \cot{\left (x \right )}\right) \sin{\left (x \right )} \cos{\left (x \right )}$$