Question

HP persamaan cos 2x° - cos x° + 1 = 0 pada interval 0 <= x <= 360 adalah ..
A. {0, 60, 120, 240}
B. {30, 90, 120, 240}
C. {30, 120, 240, 300}
D. {60, 90, 270, 300}
E. {90, 120, 240, 300}

Answer 1

Cos2x - cosx + 1 = 0
cos(x + x) - cosx + 1 = 0
cosxcosx - sinxsinx - cosx + 1 = 0
cos²x - sin²x - cosx + 1 = 0
cos²x - (1 - cos²x) - cosx + 1 = 0
cos²x + cos²x - 1 + 1 - cosx = 0
2cos²x - cosx = 0
cosx(2 cosx - 1) = 0

cosx = 0

2cosx - 1 = 0
2cosx = 1
cosx = 1/2

Jadi nilainya akan memenuhi jika cosx = 0 dan cosx = 1/2
= 60, 90, 270, 300
---> D.