5-cosx = (-корень из 6 sinx) ^2

5 - Cosx = (- √ 6 Sinx) ^2

5 - Cosx = 6Sin ²x

6Sin²x + Cosx - 5 = 0

6 (1 - Cos²x) + Cosx - 5 = 0

6 - 6Cos²x + Cosx - 5 = 0

6Cos²x - Cosx - 1 = 0

Cosx = t

6t² - t - 1 = 0

D = 1 - 4*6 * (-1) = 25

t₁ = (1 + 5) / 12 = 1/2; t₂ = (1 - 5) / 12 = - 1/3

Сosx = 1/2 Cosx = - 1/3

x = + - π/3 + 2πk, k ∈Z x = + - arcCos (-1/3) + 2πn, n ∈ Z