Ответ:
a)
x₁ = π/6 + 2πn n∈Z
x₂ = 5π/6 + 2πk k∈Z
x₃ = 2π/3 + 2πm m∈Z
x₄ = - 2π/3 + 2πp p∈Z
б)
-11π/6; -7π/6; x₃ = -4π/3;
Объяснение:
sin 2x + sin x = cos x + 0.5
2siv x · cos x + sin x = cos x + 0.5
2sin x (cos x + 0.5) - (cos x + 0.5) = 0
(2sin x -1)(cos x + 0.5) = 0
1. 2 sin x = 1
sin x = 0.5
x₁ = π/6 + 2πn n∈Z
x₂ = 5π/6 + 2πk k∈Z
1.1. -2.5π ≤ π/6 + 2πn ≤ -π
-16/6 ≤ 2n ≤ -7/6
-16/12 ≤ n ≤ -7/12
n = -1
x₁ = π/6 - 2π
x₁ = -11π/6
1.2. -2.5π ≤ 5π/6 + 2πk ≤ -π
-20/6 ≤ 2k ≤ -11/6
-20/12 ≤ k ≤ -11/12
k = -1
x₂ = 5π/6 - 2π
x₂ = -7π/6
2. cos x = - 0.5
x₃ = 2π/3 + 2πm m∈Z
x₄ = - 2π/3 + 2πp p∈Z
2.1. -2.5π ≤ 2π/3 + 2πm ≤ -π
-19/6 ≤ 2m ≤ -10/6
-19/12 ≤ m ≤ -10/12
m = -1
x₃ = 2π/3 - 2π
x₃ = -4π/3
2.2. -2.5π ≤ -2π/3 + 2πm ≤ -π
-11/6 ≤ 2m ≤ -2/6
-11/12 ≤ m ≤ -2/12
нет решений