4sin (2x-п/5) * cos (2x-п/5) = 1

Формула

2sinα·cosα=sin2α

2sin (4x - (2π/5)) = 1

sin (4x - (2π/5)) = 1/2

4x + (2π/5) = (π/6) + 2πk, k∈ Z или 4x = (2π/5) = (5π/6) + 2πn, n∈ Z

4x = (2π/5) + (π/6) + 2πk, k∈ Z или 4x = (2π/5) + (5π/6) + 2πn, n∈ Z

x = (17π/120) + (π/2) ·k, k∈ Z или x = (37π/120) + (π/2) ·n, n∈ Z

О т в е т. (17π/120) + (π/2) ·k, (37π/120) + (π/2) ·n, k, n∈ Z