1)
sinx = t, -1 ≤ t ≤ 1
4t² + 11t - 3 = 0
D = 121 + 48 = 169
t₁ = (-11-13)/8 = -3 < - 1 - не удовлетворяет ОДЗ
t₂ = (-11 + 13)/4 = 0.5
sinx = 0.5
x = (-1)ⁿ * π/3 + πn, n∈Z
2)
cosx = t, -1 ≤ t ≤ 1
2t² - t - 3 = 0
D = 1 + 24 = 25
t₁ = (1+5)/4 = 6/4 > 1 - не удовлетворяет ОДЗ
t₂ = (1 - 5)/4 = -1
cosx = -1
x = π + 2πn, n∈Z
3)
cos²x = 1 - sin²x
5 - 5sin²x + 6sinx - 6 = 0
5sin²x - 6sinx + 1 = 0
sinx = t, -1 ≤ t ≤ 1
5t² - 6t + 1 = 0
D = 36 - 20 = 16
t₁ = (6+4)/10 = 1
t₂ = (6-4)/10 = 0.2
sinx = 1
x₁ = π/2 + 2πn, n∈Z
sinx = 0.2
x₂ = (-1)ⁿarcsin(0.2) + πn, n∈Z
0 ≤ arcsin(0.2) ≤ π/2