6Cos²x +5Sinx -2 = 0
6(1 - Sin²x) + 5Sinx -2 = 0
6 -6Sin²x +5Sinx -2 = 0
-6Sin²x +5Sinx +4 = 0
Sinx = t
-6t² +5t +4 = 0
D = 25 -4*(-6)*4 = 121
t₁ = (-5 +11)/(-12) = 6/12 = 1/2
t₂ = (- 5 - 11)/(-12) = 16/12 = 4/3
a) t₁ = 1/2
Sinx = 1/2
x = (-1)ⁿ arcSin1/2 + nπ, n ∈Z
x = (-1)ⁿ π/6 + nπ, n ∈Z
б) t₂ = 4/3
Sinx = 4/3
∅
Ответ: x = (-1)ⁿ π/6 + nπ, n ∈Z