(tg55° - tg10°) / (1 + tg55° * tg10°). Created by alligator02nd. algebra-ru

(1 + tg55° * tg10°)...

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$\dfrac{tg55^{\circ} - tg10^{\circ}}{1 + tg55^{\circ} \cdot tg10^{\circ}} = tg(55^{\circ} - 10^{\circ}) = tg45^{\circ} = 1$
Формула:
$tg( A - B) = \dfrac{tgA - tgB}{1 + tgA \cdot tgB }$

2 votes Thanks 3

alligator02nd Спасибо большое, что напомнили данную формулу,совсем из головы вылетела...

Dимасuk не за что

Санечка69

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Известно тождество: tg(α - β) = (tgα - tgβ)/(1 + tgα · tgβ)
Согласно ему, если α = 55°, а β = 10°, получим:
(tg55° - tg10°)/(1 + tg55° · tg10°) = tg(55° - 10°) = tg45° = 1

1 votes Thanks 1

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