4 cos^3x+5sin2x+2cosx=0

4cos^3 (x) + 10sinx cosx + 2cosx = cosx (4cos^2 (x) + 10sinx + 2) = cosx (4 - 4sin^2 (x) + 10sinx + 2) =

-2cosx (2sin^2 (x) - 5sinx - 3) = 0

cosx = 0

x = pi/2 + pi*n

или

2sin^2 (x) - 5sinx - 3 = 0

D = 49

sinx = (5 + 7) / 4 = 3

нет решений

sinx = - 1/2

x = - pi/6 + 2pi*n

x = - 5pi/6 + 2pi*n

Ответ: x = pi/2 + pi*n; x = - pi/6 + 2pi*n; x = - 5pi/6 + 2pi*n, n принадлежит Z.