1/2 (cos (10x - 2x) - cos (10x + 2x)) = 1/2 (cos (8x - 4x) - cos (8x + 4x)) cos 8x - cos 12x = cos 4x - cos 12x cos 8x - cos 4x = 0 - 2 sin ((8x - 4x)/2) · sin ((8x + 4x)/2) = 0 sin 2x · sin 6x = 0 sin 2x = 0 или sin 6x = 0 2x = πn 6x = πk x = πn/2 x = πk/6 - π/6 ≤ πn/2 ≤ π/2 - π/6 ≤ πk/6 ≤ π/2 - π ≤ 3πn ≤ 3π -π ≤ πk ≤ 3π - 1/3 ≤ n ≤ 1 -1 ≤ k ≤ 3 n = 0 ⇒ x = 0 k = -1 x = - π/6 n = 1 x = π/2 k = 0 x = 0 k = 1 x = π/6 k = 2 x = π/3 k = 3 x = π/2 ответ: - π/6; 0; π/6; π/3; π/2
cos 8x - cos 12x = cos 4x - cos 12x
cos 8x - cos 4x = 0
- 2 sin ((8x - 4x)/2) · sin ((8x + 4x)/2) = 0
sin 2x · sin 6x = 0
sin 2x = 0 или sin 6x = 0
2x = πn 6x = πk
x = πn/2 x = πk/6
- π/6 ≤ πn/2 ≤ π/2 - π/6 ≤ πk/6 ≤ π/2
- π ≤ 3πn ≤ 3π -π ≤ πk ≤ 3π
- 1/3 ≤ n ≤ 1 -1 ≤ k ≤ 3
n = 0 ⇒ x = 0 k = -1 x = - π/6
n = 1 x = π/2 k = 0 x = 0
k = 1 x = π/6
k = 2 x = π/3
k = 3 x = π/2
ответ: - π/6; 0; π/6; π/3; π/2