1. Cot(x/2) × Sin(x) ≥ 2π
2. |Sin(x) + Cos(x)| < 1/√2
3. Sin(2x) - √3Cos(2x) > √2
4. -2 ≤ Tan(x) < 1
5. 2Sin²(x) - 5Sin(x) + 2 > 0
6. Cot²(x) - Cot(x) - 2 ≤ 0
7. Cos²(2x)/Cos²(x) ≥ 3Tan(x)
8. Sin⁴(x) + Cos⁴(x) ≥ √3/2

Question

Алгебра: 1. Cot(x/2) × Sin(x) ≥ 2π 2. |Sin(x) + Cos(x)| 1/√2 3. Sin(2x) - √3Cos(2x) √2 4. -2 ≤ Tan(x) 1 5. 2Sin²(x) - 5Sin(x) + 2 0 6. Cot²(x) - Cot(x) - 2 ≤ 0 7. Cos²(2x)/Cos²(x) ≥ 3Tan(x) 8. Sin⁴(x) + Cos⁴(x) ≥ √3/2

yana1028 · Accepted Answer

Решение
1) 2sin x-1=0
sinx = 1/2
x = (-1)^n arcsin(1/2) + πk, k∈Z
x = (-1)^n (π/6) + πk, k∈Z
2) cos(2x+П/6)+1=0
cos(2x+П/6) = - 1
2x+П/6 = π + 2πn, n∈Z
2x = π - π/6 + 2πn, n∈Z
2x = 5π/6 + 2πn, n∈Z
x = 5π/12 + πn, n∈Z
3) 6sin²x - 5cosx + 5 = 0
6(1 - cos²x) - 5cosx + 5 = 0
6 - 6cos²x - 5cosx + 5 = 0
6cos²x + 5cosx - 11 = 0
cosx = t, ItI ≤ 1
6t² + 5t - 11 = 0
D = 25 + 4*6*11 = 289
t₁ = (- 5 - 17)/12
t₁ = - 22/12
t₁ = -11/6
t₁ = - 1 (5/6) не удовлетворяет условию ItI ≤ 1
t₂ = (- 5 + 11)/12
t₂ = 1/2
cosx = 1/2
x = (+ -)arccos(1/2) + 2πm, m∈Z
x = (+ -) *(π/3) + 2πm, m∈Z

1. Cot(x/2) × Sin(x) ≥ 2π 2. |Sin(x) + Cos(x)| < 1/√2 3. Sin(2x) - √3Cos(2x) > √2 4. -2 ≤ Tan(x) < 1 5. 2Sin²(x) - 5Sin(x) + 2 > 0 6. Cot²(x) - Cot(x) - 2 ≤ 0 7. Cos²(2x)/Cos²(x) ≥ 3Tan(x) 8. Sin⁴(x) + Cos⁴(x) ≥ √3/2

MOGZ ответил

1. Cot(x/2) × Sin(x) ≥ 2π
2. |Sin(x) + Cos(x)| < 1/√2
3. Sin(2x) - √3Cos(2x) > √2
4. -2 ≤ Tan(x) < 1
5. 2Sin²(x) - 5Sin(x) + 2 > 0
6. Cot²(x) - Cot(x) - 2 ≤ 0
7. Cos²(2x)/Cos²(x) ≥ 3Tan(x)
8. Sin⁴(x) + Cos⁴(x) ≥ √3/2