jangan lupa pake jalan kak:)

[tex]\displaystyle \sin(a+b)=\frac12\\\sin a\cos b+\cos a\sin b=\frac12\\\frac12\sqrt3+\cos a\sin b=\frac12\\\cos a\sin b=\frac12-\frac12\sqrt3\\\\\sin(a-b)=\sin a\cos b-\cos a\sin b\\\sin(a-b)=\frac12\sqrt3-\frac12+\frac12\sqrt3\\\sin(a-b)=\sqrt3-\frac12\\\\\frac{\sin(a-b)}{\sin(a+b)}=\frac{\sqrt3-\frac12}{\frac12}\\\boxed{\boxed{\frac{\sin(a-b)}{\sin(a+b)}=2\sqrt3-1}}[/tex]

Bab Trigonometri
Matematika SMA Kelas X

α = a
β = b

sin (a + b) = 1/2
sin a cos b + cos a . sin b = 1/2
1/2 √3 + cos a . sin b = 1/2
cos a . sin b = 1/2 - 1/2 √3

(sin (a - b)) / (sin (a + b))
= (sin a . cos b - cos a . sin b) / (1/2)
= (1/2 √3 - 1/2 + 1/2 √3) . 2
= 2 . (-1/2 + √3)
= 2√3 - 1

jawabannya A