Предмет: Математика, автор: katylik1997

tg²α+ctg²α,если tg α+ctg α=4

Ответы

Автор ответа: artalex74

Для начала рассмотрим tg α+ctg α = 4. Обе части возводим в квадрат:
(tg α+ctg α)² = 16, т.е.
tg² α + 2tg α ctg α + ctg² α = 16
tg² α + 2 + ctg² α = 16
tg² α + ctg² α = 16 - 2 = 14
Ответ: 14.

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