Question

sin 4x + 2sin² 7x = 1

Answer 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