Verified answer

1) sin 3x*cos x - cos 3x*sin x = 1

sin (3x - x) = sin 2x = 1

2x = π/2 + 2π*k; k ∈ Z

x = π/4 + π*k; k ∈ Z

2) sin x*cos x = 0

1/2*2sin x*cos x = 1/2*sin 2x = 0

sin 2x = 0

2x = π*k, k ∈ Z

x = π/2*k, k ∈ Z