Помогите решить 9tg^2x+ctg^2x=6. Буду благодарен!

Question

Помогите решить 9tg^2x+ctg^2x=6. Буду благодарен!

Answer 1

9tg²x + Ctg²x = 6 | * tg²x ≠ 0
9tg^4x +1 = 6tg²x
tg²x = y
9y² -6y +1 = 0
(3y -1)² = 0
3y -1 = 0
3y = 1
y = 1/3
tg²x = 1/3
tgx = +-√1/3 = +- √3/3
x = +-π/6 + πk , k ∈ Z