1.
sin⁴x + cos⁴x = 1 - cos²x, x ∈ [π/2; 2π]
sin⁴x + cos⁴x = sin²x
sin²x·(sin²x - 1) + cos⁴x = 0
cos⁴x - sin²x·cos²x = 0
cos²x·(cos²x - sin²x) = 0
cos²x · cos 2x = 0
cos x = 0 или cos 2x = 0
x = π/2 + πk, k ∈ Z 2x = π/2 + πn, n ∈ Z
x = π/4 + πn/2, n ∈ Z
На указанном промежутке: x ∈ {π/2; 3π/4; 5π/4; 3π/2; 7π/4}.
2.
sin⁴x + cos⁴x = 1 - 3/2·sin²x, x ∈ [π/2; 2π]
2sin⁴x + 2cos⁴x = 2 - 3sin²x
2sin⁴x + 2cos⁴x = 2cos²x - sin²x
2sin⁴x + 2cos⁴x - 2cos²x = -sin²x
2sin⁴x + 2cos²x·(cos²x - 1) = -sin²x
2sin⁴x - 2sin²x·cos²x = -sin²x
2sin²x·(sin²x - cos²x) = -sin²x
2sin²x·cos 2x = -sin²x
sin²x·(1 + 2cos 2x) = 0
sin x = 0 или 1 + 2cos 2x = 0
x = πk, k ∈ Z 2cos 2x = -1
cos 2x = -1/2
2x = (+/-) 2π/3 + 2πn, n ∈ Z
x = (+/-) π/3 + πn, n ∈ Z
На указанном промежутке: x ∈ {2π/3; π; 4π/3; 5π/3; 2π}.