himpunan penyelesaian persamaan cos 2x - 2 cos x = -1 , 0 ≤ x ≤ 2 phi

Diketahui rumus cos2x = 2cos²x - 1

cos2x - 2cosx = -1
2cos²x - 1 - 2cosx = -1
2cos²x - 2cosx = 0

Misalkan cosx = p

2p² - 2p = 0
2p(p - 1) = 0

p = 0 atau p = 1
cosx = 0 atau cosx = 1


Untuk cosx = 0, maka...

cosx = 0
cosx = cos90°
      x = 90° + k . 360°
      x = 90°
      x = 1/2π

cosx = 0
cosx = cos90°
      x = -90° + k . 360°
      x = 270°
      x = 3/2π


Untuk cosx = 1, maka...

cosx = 1
cosx = cos0°
      x = 0° + k . 360°
      x = 0°, 360°
      x = 2π

cosx = 1
cosx = cos0°
      x = -0° + k . 360°
      x = 0°, 360°
      x = 2π

HP = {1/2π, 3/2π, 2π}