Y = (cosx) / (sin^2 x) * tg x (π/2-x)

Cosx * ((sinx/cosx) - cosx) = - sin^2 (x)

sinx - cos^2 (x) + sin^2 (x) = 0

sinx - 1 + sin^2 (x) + sin^2 (x)) = 0

2sin^2 (x) + sinx - 1 = 0

замена: sinx = t ∈[-1; 1]

2t^2 + t - 1 = 0, D = 1 + 8 = 9

t1 = (-1-3) / 4 = - 4/4 = - 1

t2 = (-1+3) / 4 = 2/4 = 1/2

1) sinx = - 1,

x = - π/2 + 2πk, k∈Z

2) sinx = 1/2

x = π/6 + 2πk, k∈Z

x = 5π/6 + 2πk, k∈Z