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<br>-7π/2 - π/4 < πk/2 < -2π - π/4<br>-15π/4 < πk/2 < -9π/4<br>-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