4) 2(1 - Cos²x) - Cosx -1 = 0
2 - 2Cos²x - Cosx -1 = 0
-2Cos²x - Cosx +1 = 0
2Cos²x + Cosx -1 = 0
Cosx = t
2t² +t -1 = 0
D = 9
t₁ = (-1+3)/4 = 1/2 t₂ = (-1 -3)/4 = -1
Cosx = 1/2 Cos x = -1
x = +-arcCos1/2 + 2πk, k ∈Z x = π + 2πn , n ∈Z
x = +-π/3 + 2πk , k ∈Z
5)числитель = 2Sin2αCosα - 2Sin2α = 2Sin2α(Cosα -1)
знаменатель = 2Cos2αCosα -2Cos2α = 2Cos2α(Cosα -1)
после деления ответ:tg2α
6)2SinxCosx - Cosx = 2Sinx -1
Cosx(2Sinx -1) -(2Sinx -1) = 0
(2Sinx-1)(Cosx -1) = 0
2Sinx -1=0 или Соs x -1 = 0
Sinx = 1/2 Cosx = 1
x = (-1)ⁿπ/6 + nπ, n ∈Z x = π +2πk , k ∈Z