tolong di jawab ya cos 2x +7 cos x-3=0 tentukan nilai x

Bab Trigonometri
Matematika SMA Kelas X

cos 2x + 7 cos x - 3 = 0
2 cos² x - 1 + 7 cos x - 3 = 0
2 cos² x + 7 cos x - 4 = 0
(2 cos x - 1 ) (cos x + 4) = 0
2 cos x - 1 = 0
cos x = 1/2
x = 60° dan 300°

cos x + 4 = 0
cos x = - 4 (tidak memenuhi)

cos 2x + 7 cos x - 3 = 0
(cos^2 x - sin^2 x) + 7 cos x - 3 = 0
cos^2 x - sin^2 x + 7 cos x - 3 + 1 = 0 + 1
cos^2 x + 1 - sin^2 x + 7 cos x - 3 = 1
cos^2 x + cos^2 x + 7 cos x - 4 = 0
2 cos^2 x + 7 cos x - 4 = 0
Misal : cos x = a, maka :
2a^2 + 7a - 4 = 0
(2a - 1) (a+4) = 0

2a - 1 = 0
2a = 1
a = 1/2
cos x = 1/2
x = 60 derajat


atau

a + 4 = 0
a = -4
cos x = -4
( tidak memenuhi syarat )

Jadi, nilai x = 60