Himpunan penyelesaian dari √3 sin 2x + 2 cos² x = -1

Gunakan sifat

a.sin x + b.cos x = c
k.sin(x - @) = c

Dengan :
k = √(a²+b²)
tan @ = a/b

√3 .sin 2x + 2 .cos² x = -1
√3 .sin 2x + 2 .cos² x - 1 = -1 - 1
√3 .sin 2x + cos 2x = -2
√((√3)²+(1)²) .sin(2x - @) = -2
2 .sin (2x - @) = -2
sin (2x - @) = -1
**
tan @ = √3/1 = √3
@ = 60° atau @ = 240°
**

(1)
sin (2x - 60°) = -1
sin (2x - 60°) = sin 270°
..(1,i)
2x - 60° = 270° ± k.360°
2x = 330° ± k.360°
x = 115° ± k.180°
..(1,ii)
2x - 60° = (180°-270°) ± k.360°
2x = -30° ± k.360°
x = -15° ± k.18°

(2)
sin (2x - 240°) = -1
sin (2x - 240°) = sin 270°
..(2,i)
2x - 240° = 270° ± k.360°
2x = 30° ± k.360°
x = 15° ± k.180°
..(2,ii)
2x - 240° = (180°-240°) ± k.360°
2x = 180° ± k.360°
x = 90° ± k.180°

Jadi, penyelesaiannya ada empat (tertera di atas).