tg60 * tg50 * tg45 * tg40 * tg30. Created by Elchin9. algebra-ru

tg60 * tg50 * tg45 * tg40 * tg30...

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tg60 * tg50 * tg45 * tg40 * tg30

Verified answer

$tg50=ctg40\\
ctg40*tg40=1\\
\\
tg60=\sqrt{3}\\
tg45=1\\
tg30=\frac{1}{\sqrt{3}}\\
1*\sqrt{3}*1*\frac{1}{\sqrt{3}}=1$

Ответ $1$

8 votes Thanks 9

riskova63 Tg60 = √3, tg45 = 1, tg30 = 1/√3. Найдем tg50 · tg40 = tg(90 - 40) * tg40 = ctg40 * tg 40 = 1. Значит данное произведение равно √3 * 1 * 1 * 1/√3 = 1.

3 votes Thanks 5

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