Tentukan himpunan penyelesaiannya! 3 tan²x - secan²x - 5 = 0, 0 ≤ x ≤ 2π

TriGonoMetRi

Interval : 0 ≤ x ≤ 2π

3 tan² x - secan² x - 5 = 0
3 sin² x - 5 cos² x - 1 = 0
3 sin² x - 5(1 - sin² x) - 1 = 0
8 sin² x - 6 = 0
sin² x = 6/8
sin x = ± √(6/8)
sin x = 1/2 √3
x = 60° , 120°

sin x = -1/2 √3
x = 240° , 300°

HP = {1/3 π , 2/3 π , 4/3 π , 5/3 π}

jawab

3 tan² x - sec² x - 5 = 0
3 (sin² x)/cos² x - 1/cos² x  - 5 = 0 }kalikan cos² x
3 sin² x - 1 - 5 cos² x = 0
3 sin² x- 1 - 5(1- sin² x) = 0
3 sin²x - 1 - 5 + 5 sin² x - 0
8 sin² x  - 6 = 0
sin² x = 6/8 = 3/4
sin x = 1/2 √ 3 atau sin x = - 1/2 √3

0 ≤  x  ≤ 2π
sin  x = 1/2 √3 =sin 60 = sin 120
x = 60, 120
x = 1/3 π , 2/3 π

sin x = - 1/2√3 = -sin 60 = sin 240 = sin 300
x = 240, 300
x= 4/3 π, 5/3 π

x = (1/3π, 2/3 π, 4/3 π, 5/3 π)