1)
1 - sin²x + sinx - 1/4 = 0
4sin²x - 4sinx - 3 = 0
D/4 = 4 + 12 = 16
sinx = 3/2 нет корней
sinx = - 1/2
x = - π/6 + 2πn x = 7π/6 + 2πk
2)
sin4x/cos4x - 2sin4x·cos4x = 0
sin4x (1/cos4x - 2cos4x) = 0
sin4x = 0 1 - 2cos²4x = 0
4x = πn cos²4x = 1/2
x = πn/4 cos4x = 1/√2 cos4x = - 1/√2
4x = π/4 + πk/2
x = π/16 + πk/8
3)
cos2x + 1 - cos6x = 1
cos2x - cos6x = 0
- 2sin(-2x)sin4x = 0
sin2x = 0 sin4x = 0
2x = πn 4x = πk
x = πn/2 x = πk/4
Первая группа корней включена во вторую.
Ответ: πk/4