Jawaban:

Ingat!

sin²x + cos²x = 1

Jika sin x = sin a, maka x = a ± k . 360° atau x = (180° - a) + k . 360°

Maka:

cos²x - sin²x + sinx - 1 = 0

cos²x - sin²x + sinx - (sin²x + cos²x) = 0

cos²x - sin²x + sinx - sin²x - cos²x = 0

-2sin²x + sinx = 0

sinx(-2sinx + 1) = 0

Sehingga:

→ sinx = 0

sinx = sin 0°

x = 0° + k.360°

k = 0 → x = 0° + 0 . 360° = 0° + 0° = 0° (memenuhi)

k = 1 → x = 0° + 1 . 360° = 0° + 360° = 360° (tidak memenuhi)

x = (180° - 0°) + k . 360°

x = 180° + k . 360°

k = 0 → x = 180° + 0 . 360° = 180° + 0° = 180° (memenuhi)

k = 1 → x = 180° + 1 . 360° = 180° + 360° = 540° (tidak memenuhi)

→ -2sinx + 1 = 0

-2sinx = -1

sinx = (-1)/(-2)

sinx = 1/2

sinx = sin 30°

x = 30° + k . 360°

k = 0 → x = 30° + 0 . 360° = 30° + 0° = 30° (memenuhi)

k = 1 → x = 30° + 1 . 360° = 30° + 360° = 390° (tidak memenuhi)

x = (180° - 30°) + k . 360°

x = 150° + k . 360°

k = 0 → x = 150° + 0 . 360° = 150° + 0° = 150° (memenuhi)

k = 1 → x = 150° + 1 . 360° = 150° + 360° = 510° (tidak memenuhi)

Kesimpulan :

Jadi, nilai x yang memenuhi persamaan tersebut adalah {0°, 30°, 150°, 180°}.

Semoga membantu!!!

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