Как отобрать корни на числовой окружности?

Приведем к общему знаменателю cos^2 (x) * sin^2 (x)

(sin^2 (x) - 4cos^2 (x) + 6cos^2 (x) * sin^2 (x)) / (cos^2 (x) * sin^2 (x)) = 0

дробь равна 0, когда числитель равен 0, знаменатель не равен 0.

sin^2 (x) - 4cos^2 (x) + 6cos^2 (x) * sin^2 (x) = 0

(sin^2 (x) - cos^2 (x)) + (6cos^2 (x) * sin^2 (x) - 3cos^2 (x)) = 0

- (cos^2 (x) - sin^2 (x)) + 3cos^2 (x) * (2sin^2 (x) - 1) = 0

-cos (2x) - 3cos^2 (x) * cos (2x) = 0

cos (2x) * (1 + 3cos^2 (x)) = 0

1) cos (2x) = 0

2x = π/2 + πk

x = π/4 + πk/2

2) 1 + 3cos^2 (x) = 0

cos^2 (x) = - 1/3 - нет решений

Произведем отбор корней, принадлежащих промежутку x ∈ (-7π/2; - 2π)

-7π/2 < π/4 + πk/2 < - 2π

-7π/2 - π/4 < πk/2 < - 2π - π/4

-15π/4 < πk/2 < - 9π/4

-15/2 < k < - 9/2

k - целое, k = - 5; - 6; - 7

k = - 5, x = π/4 - 5π/2 = - 9π/4

k = - 6, x = π/4 - 6π/2 = - 11π/4

k = - 7, x = π/4 - 7π/2 = - 13π/4

Ответ: - 9π/4; - 11π/4; - 13π/4