Решите уравнение:

1-2cos^2 (4x-п/4) = 0

1 - 2cos² (4x - π/4) = 0

cos² (4x - π/4) = 1/2

cos (4x - π/4) = ±√2/2

1) cos (4x - π/4) = √2/2

4x - π/4 = ±π/4 + 2πn, n ∈ Z

4x = ±π/4 + π/4 + 2πn, n ∈ Z

x = ±π/16 + π/16 + πn/2, n ∈ Z

2) cos (4x - π/4) = - √2/2

4x - π/4 = ±3π/4 + 2πn, n ∈ Z

4x = ±3π/4 + π/4 + 2πn, n ∈ Z

x = ±3π/16 + π/16 + πn/2, n ∈ Z