Sin 4x + 2sin² 7x = 1

Sin4x+2sin²7x-1=0

sin4x-cos14x=0

sin4x-sin (π/2-14x) = 0

2sin (9x-π/4) cos (π/4-5x) = 0

sin (9x-π/4) = 0

9x-π/4=πn

9x=π/4+πn

x=π/36+πn/9, n∈z

cos (5x-π/4) = 0 (косинус четная функция)

5x-π/4=π/2+πk

5x=3π/4+πk

x=3π/20+πk/5, k∈z