Question

Himpunan penyelesaian persamaan cos 2x-3 cos x+2=0, 0 lebihdarisamadengan x lebihdarisamadengan 2pi ...

Answer 1

Cos2x - 3cosx + 2 = 0
2cos²x-1 - 3cosx + 2 = 0
2cos²x - 3cosx + 1 = 0
(2cosx-1) (cosx-1) = 0

#
2cosx-1 = 0
2cosx = 1
cosx = 1/2
cosx = cos 60 
x = 60+k.360          atau x = -60+k.360
k = 0 --> x = 60              k = 0 --> x = -60 (bukan penyelesaian)
             x = π/3             k = 1 --> x = 300
                                                  x = 5π/3

#
cosx-1 = 0
cosx = 1
cosx = cos 0
x = 0+k.360            atau x = -0+k.360 (penyelesaian sm dgn sblm)
k = 0 --> x = 0
k = 1 --> x = 360
             x = 2π

jadi Hp = {0,π/3,5π/3,2π}

semoga membantu ya :)