1) a) Sinx = a
x = (-1)ⁿarcSina +nπ, n ∈Z
б) tgx = a
x = arctga + πk , k ∈Z
2)a)2Cosx - √2 = 0
Cosx = √2/2
x = +-π/4 + 2πk , k ∈Z
б) 3Ctgx +1 ≥ 0
Ctgx ≥ -1/3
-arcCtg1/3 + πk ≤ x < 0 + πk , k ∈Z
3)2Cos5x*Cos6x + Cos5x = 2Cos6x +1
2Cos5x*Cos6x + Cos5x - ( 2Cos6x +1) = 0
Cos5x(2Cos6x +1) - ( 2Cos6x +1) = 0
( 2Cos6x +1)(Cos5x -1) = 0
( 2Cos6x +1) = 0 или Сos5x -1 = 0
Cos6x = -1/2 Cos5x = 1
6x = +-2π/3 +2πk , k ∈Z 5x = 2πn , n ∈Z
x = +- π/9 + πk/3 , k ∈Z x = 2πn/5, n ∈Z
4)a) 6Sin²x -5Sinx +1 = 0
Sinx = t
6t² -5t +1 = 0
t₁ = 1/2, t₂= 1/3
a) Sinx = 1/2 б) Sinx = 1/3
x = (-1)ⁿπ/6 + πn, n ∈Z x = (-1)ᵇarcSin(1/3) + bπ, b∈Z
б) 6Cos²x - 5Sinx +5 = 0
6(1 - Sin²x) -5Sinx +5 = 0
6 -6Sin²x -5Sinx +5 = 0
-6Sin²x - 5Sinx +11 = 0
Sinx = t
-6t² -5t +11 = 0
D = 289
t₁ = -11/6 t₂= 1
Sinx = -11/6 Sinx = 1
∅ x = π/2 +2πk , k ∈Z
в) Cos2x +Sinx = 0
1 - 2Sin²x +Sinx = 0
Sinx = t
-2t² +t +1 = 0
D = 9
t₁= -1/2 t₂ = 1
Sinx = -1/2 Sinx = 1
x = (-1)ⁿ⁺¹π/6 + nπ, n ∈Z x = π/2 + 2πk , k ∈Z