cos2x+sin²x = 0,75
cos²x - sin²x + sin²x = 0.75
cos²x = 0.75
cosx = ±√0.75 = ±0.5√3
1) cosx = -0.5√3
x₁ = 5π/6 + 2πn
x₂ = -5π/6 + 2πn
n =1 x₁ = (2 + 5/6) π x∉[π; 5π/2]
x₂ = (2- 5/6) π = 7π/6 x∈[π; 5π/2]
n =2 x₁ = (4 + 5/6) π x∉[π; 5π/2]
x₂ = (4- 5/6) π x∉[π; 5π/2]
2) cosx = 0.5√3
x₁ = π/6 + 2πn
x₂ = -π/6 + 2πn
n =1 x₁ = (2 + 1/6) π = 13π/6 x∈[π; 5π/2]
x₂ = (2 - 1/6) π = 11π/6 x∈[π; 5π/2]
n =2 x₁ = (4 + 1/6) π x∉[π; 5π/2]
x₂ = (4- 1/6) π x∉[π; 5π/2]
ответ: x = 7π/6; 11π/6; 13π/6
б) 3 остаток 10
в) 3 остаток 2
г) 9 остаток 1