Question

Решить: $3 tg^{2} x -4tgx-7=0$
И найти все X на промежутке: [-П/2 ; П]

Answer 1

3tg^2x - 4tgx - 7 = 0
tgx = t
3t^2 - 4t - 7 = 0
(3t - 7)(t + 1) = 0
t = -1 -> tgx = -1 -> x = -П/4 + Пk = { [-П/2; П } = -П/4, 3П/4
3t = 7 -> tgx = 7/3 -> x = arctg(7/3) + Пk = { [-П/2; П } = arctg(7/3)
x = -П/4, arctg(7/3), 3П/4