Ответ:

8. 1-Б; 2-Г; 3-А; 4-В.

9. 1-Д; 2-Б; 3-Г; 4-А.

Подробнее объяснение:

8. 1) 2cosx = 1

cosx = 1/2

x = ± arccos1/2 + 2πn, n є Z

x = ± π/3 + 2πn, n є Z. Б.

2) 2cosx/2 = 1

cosx/2 = 1/2

x/2 = ± arccos1/2 + 2πn, n є Z

x/2 = ± π/3 + 2πn, n є Z.

x = ± 2π/3 + 4πn, n є Z. Г.

3) cos2x = 1

2x = ± arccos1/2 + 2πn, n є Z

2x = ± π/3 + 2πn, n є Z.

x = ± π/6 + πn, n є Z. А.

4) cosx/2 = 1

x/2 = 2πn, n є Z.

x = 4πn, n є Z. В.

Відповідь: 1-Б; 2-Г; 3-А; 4-В.

9. 1) sin2x = 0. [0; 2π] sinx є [-1; 1]

2x = πn, n є Z

x = πn/2, n є Z n = 0, x = 0 +

n = 1, x = π/2. +

n = 2, x = π +

n = 3, x = 3π/2 +

n = 4, x = 2π. +

n = 5, x = 5π/2 -

П'ять коренів. Д.

2) sin2x = 1. [0; 2π]

2x = π/2 + 2πk, k є Z.

x = π/4 + πk, k є Z.

k = 0, x = π/4. +

k = 1, x = 5π/4. +

k = 2, x = 9π/4. -

Два корені. Б.

3) cos2x = 0. [0; 2π]

2x = π/2 + πm, m є Z.

x = π/4 + πm/2, m є Z.

m = 0, x = π/4. +

m = 1, x = 3π/4. +

m = 2, x = 5π/4. +

m = 3, x = 7π/4. +

m = 4, x = 9π/4. -

Чотири корені. Г.

4) tgx/2 = 1. [0; 2π]

x/2 = arctg1 + πt, t є Z.

x/2 = π/4 + πt, t є Z.

x = π/2 + 2πt, t є Z.

t = 0, x = π/2 . +

t = 1, x = 5π/2. -

Один корінь. А.

Відповідь: 1-Д; 2-Б; 3-Г; 4-А.