если tg & + ctg &= 2,
то значение выражения
tg^3 & + ctg^3 &=?
tg³α + ctg³α = (tg α + ctg α) * (tg²α - tg α * ctg α + ctg²α) =
(tg α + ctg α) * (tg²α + 2 * tg α * ctg α + ctg²α - 3 * tg α * ctg α) =
(tg α + ctg α) * ((tg α + ctg α)² - 3) = 2 * (2² - 3) = 2
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Verified answer
tg³α + ctg³α = (tg α + ctg α) * (tg²α - tg α * ctg α + ctg²α) =
(tg α + ctg α) * (tg²α + 2 * tg α * ctg α + ctg²α - 3 * tg α * ctg α) =
(tg α + ctg α) * ((tg α + ctg α)² - 3) = 2 * (2² - 3) = 2