Jika 3 cos^2 2x + 4 cos 2x – 4 = 0 . Nilai cos x =

TriGonoMetRi

3 cos² 2x + 4 cos 2x – 4 = 0
(3 cos 2x – 2)(cos 2x + 2) = 0

Yg memenuhi :
3 cos 2x – 2 = 0
cos 2x = 2/3

cos 2x = 2/3
2 cos² x – 1 = 2/3
2 cos² x = 1 + 2/3
2 cos² x = 5/3
cos² x = 5/6
cos x = √(5/6)
cos x = 1/6 √30 ✔
atau
cos x = -1/6 √30 ✔

Bab Trigonometri
Matematika SMA Kelas X

3 cos² 2x + 4 cos 2x – 4 = 0
(3 cos 2x – 2) (cos 2x + 2) = 0
3 cos 2x – 2 = 0
3 cos 2x = 2
cos 2x = 2/3
2 cos² x – 1 = 2/3
2 cos² x = 1 + 2/3
2 cos² x = 3/3 + 2/3
cos² x = (5/3) . 1/2
cos x = +-√(5/6)
atau
cos x = +-√5 : √6
cos x = +- (1/6) √30

cos 2x + 2 = 0
2 cos² x – 1 = -2
2 . cos² x = -2 + 1
cos² x = -1/2
cos x = √(-1/2) → bilangan tidak real / imajiner

HP = { -√(5/6), √(5/6) }
atau
HP = { (-1/6) √30, (1/6) √30 }