4cos²x/sinx + 4cosx/sinx + sinx = 0
приводим к общему знаменателю
(4сos²x + 4cosx + sin²x)/sinx = 0
sinx ≠ 0
(4сos²x + 4cosx + sin²x) = 0
sin²x = 1-cos²x
4cos²x + 4cosx + 1 -cos²x
3cos²x + 4cosx + 1 = 0
cosx = a
3a² + 4a + 1 = 0
-4±√(16 - 12)/6
a1 = -4 + 2 / 6 = -1/3
a2 = -4-2 / 6 = -1
1) cosx = -1/3
x = ±(π-arccos1/3) + 2πn
2) cosx = -1
x = π + 2πn