Dik sin alpa cos beta = 2/5 dan (alpa + beta) = 5pi/6 tentukan nilai sin (alpa - beta)

Kelas 11 Matematika
Bab Trigonometri Lanjut

α = a
β = b

a + b = 5π/6
sin (a + b) = sin 5π/6
sin a cos b + cos a sin b = 1/2
2/5 + cos a sin b = 1/2
cos a sin b = 1/2 - 2/5
cos a sin b = 5/10 - 4/10
cos a sin b = 1/10

sin (a - b) = sin a cos b - cos a sin a
sin (a - b) = 2/5 - 1/10
sin (a - b) = 4/10 - 1/10
sin (a - b) = 3/10