Способом разложения на множители:

4sin⁴ (x-π) + cos² (3π/2 - 2x) = 2 [-5π/2; - 3π/2]

4Sin⁴ (x-π) + Cos² (3π/2-2x) = 2

4Sin⁴x + Sin²2x = 2

4Sin⁴x + 4Sin²xCos²x = 2

4Sin²x (Sin²x + Cos²x) = 2

4Sin²x = 2

2Sin²x = 1

Sin²x = 1/2

Sinx = √2/2 Sinx = - √2/2

x = (-1) ⁿarcSin√2/2 + πn, n ∈ z x = (-1) ⁿarcSin (-√2/2) + πn, n ∈ z

x = (-1) ⁿπ/4 + πn, n ∈ z x = (-1) ⁿ (-π/4) + πn, n ∈ z

x = (-1) ⁿ⁺¹π/4 + πn, n ∈ z

Корни из заданного промежутка : - 7π/4, - 9π/4