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
НОК (60; 24; 36) = 2 * 2 * 2 * 3 * 3 * 5 = 360 - наименьшее общее кратное
30 = 2 * 3 * 5; 45 = 3 * 3 * 5; 105 = 3 * 5 * 7
НОК (30; 45; 105) = 2 * 3 * 3 * 5 * 7 = 630 - наименьшее общее кратное
80 = 2 * 2 * 2 * 2 * 5; 88 = 2 * 2 * 2 * 11; 220 = 2 * 2 * 5 * 11
НОК (80; 88; 105) = 2 * 2 * 2 * 2 * 5 * 11 = 880 - наименьшее общее кратное
36 = 2 * 2 * 3 * 3; 90 = 2 * 3 * 3 * 5; 200 = 2 * 2 * 2 * 5 * 5
НОК (36; 90; 200) = 2 * 2 * 2 * 3 * 3 * 5 * 5 = 1800 - наименьшее общее кратное
56 = 2 * 2 * 2 * 7; 140 = 2 * 2 * 5 * 7; 350 = 2 * 5 * 5 * 7
НОК (56; 140; 350) = 2 * 2 * 2 * 5 * 5 * 7 = 1400 - наименьшее общее кратное