Himpunan penyelesaian tan 2x= √3 untuk 0≤×<2π adalah

Tan 2x = √3
tan 2x = tan π/3 ………..(1)
tan 2x = tam (π – π/3) = tan 2π/3…………..(1)

Persaman (1)
tan 2x = tan π/3
 2x = π/3 + k.π
   x = π/6 + k.π/2
k=0 → x = π/6
k=1→ x = π/6 + 1.π/2 = π/6 + π/2 = 4π/6 = 2π/3
k =2→x= π/6 + 2.π/2 = π/6 + π = 7π/6
k=3→x = π/6 + 3.π/2 = π/6 + 3π/2 = 10π/6 = 5π/3

Persamaan (2)
tan 2x = tan 2π/3
  2x = 2π/3 + k.π
     x= π/3 + k.π/2
k=0→x = π/3
k=1→x = π/3 + 1.π/2 = π/3 + π/2 = 5π/6
k=2→x = π/3 + 2.π/2 = π/3 + π = 4π/3
k=3→x = π/3 + 3.π/2 = π/3 + 3π/2 = 11π/6

Hp={π/6, π/3, 2π/3, 5π/6, 7π/6, 4π/3, 5π/3, 11π/6}