sin(90+a)*sin(180-a)*(tan(180+a)+tan(270-a)) если a=3 (упростите выражение)

Дано

$$\sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )} \left(\tan{\left (- a + 270 \right )} + \tan{\left (a + 180 \right )}\right)$$
Подстановка условия
$$\sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )} \left(\tan{\left (- a + 270 \right )} + \tan{\left (a + 180 \right )}\right)$$

(sin(90 + (3))*sin(180 — (3)))*(tan(180 + (3)) + tan(270 — (3)))

$$\sin{\left (- (3) + 180 \right )} \sin{\left ((3) + 90 \right )} \left(\tan{\left (- (3) + 270 \right )} + \tan{\left ((3) + 180 \right )}\right)$$

(sin(90 + 3)*sin(180 — 3))*(tan(180 + 3) + tan(270 — 3))

$$\sin{\left (3 + 90 \right )} \sin{\left (- 3 + 180 \right )} \left(\tan{\left (- 3 + 270 \right )} + \tan{\left (3 + 180 \right )}\right)$$

(tan(183) + tan(267))*sin(93)*sin(177)

$$\left(\tan{\left (267 \right )} + \tan{\left (183 \right )}\right) \sin{\left (93 \right )} \sin{\left (177 \right )}$$
Степени
$$- \left(- \tan{\left (a — 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (a — 180 \right )} \sin{\left (a + 90 \right )}$$
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Численный ответ

(tan(180 + a) + tan(270 — a))*sin(90 + a)*sin(180 — a)

Рациональный знаменатель
$$\left(\tan{\left (a — 270 \right )} — \tan{\left (a + 180 \right )}\right) \sin{\left (a — 180 \right )} \sin{\left (a + 90 \right )}$$
Объединение рациональных выражений
$$- \left(- \tan{\left (a — 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (a — 180 \right )} \sin{\left (a + 90 \right )}$$
Общее упрощение

(-tan(180 + a) + tan(-270 + a))*sin(-180 + a)*sin(90 + a)

$$\left(\tan{\left (a — 270 \right )} — \tan{\left (a + 180 \right )}\right) \sin{\left (a — 180 \right )} \sin{\left (a + 90 \right )}$$
Соберем выражение
$$- \frac{1}{2} \cos{\left (2 a — 90 \right )} \tan{\left (a — 270 \right )} + \frac{1}{2} \cos{\left (2 a — 90 \right )} \tan{\left (a + 180 \right )} + \frac{1}{2} \cos{\left (270 \right )} \tan{\left (a — 270 \right )} — \frac{1}{2} \cos{\left (270 \right )} \tan{\left (a + 180 \right )}$$
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(tan(180 + a) + tan(270 — a))*sin(90 + a)*sin(180 — a)

$$\left(\tan{\left (- a + 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )}$$
Общий знаменатель

sin(90 + a)*sin(180 — a)*tan(180 + a) + sin(90 + a)*sin(180 — a)*tan(270 — a)

$$\sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )} \tan{\left (- a + 270 \right )} + \sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )} \tan{\left (a + 180 \right )}$$
Тригонометрическая часть

(tan(180 + a) + tan(270 — a))*sin(90 + a)*sin(180 — a)

$$\left(\tan{\left (- a + 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )}$$
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Комбинаторика

-(-tan(-270 + a) + tan(180 + a))*sin(-180 + a)*sin(90 + a)

$$- \left(- \tan{\left (a — 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (a — 180 \right )} \sin{\left (a + 90 \right )}$$
Раскрыть выражение

/ tan(180) + tan(a) -tan(270) + tan(a)
|——————- — ——————-|*(cos(180)*sin(a) — cos(a)*sin(180))*(-cos(90)*sin(a) — cos(a)*sin(90))
1 — tan(180)*tan(a) 1 + tan(270)*tan(a)/

$$\left(- \frac{\tan{\left (a \right )} — \tan{\left (270 \right )}}{\tan{\left (270 \right )} \tan{\left (a \right )} + 1} + \frac{\tan{\left (a \right )} + \tan{\left (180 \right )}}{- \tan{\left (180 \right )} \tan{\left (a \right )} + 1}\right) \left(- \sin{\left (a \right )} \cos{\left (90 \right )} — \sin{\left (90 \right )} \cos{\left (a \right )}\right) \left(\sin{\left (a \right )} \cos{\left (180 \right )} — \sin{\left (180 \right )} \cos{\left (a \right )}\right)$$
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