Jika A+B =π/6 dan sin A cos B = 1/3 maka sin A-B =......

Diketahui :
           α+β = π/6 ---> sin (π/6) = 1/2
sin α cos β = 1/3

Ditanya :
sin α-β = ???

Jawab :
  sin (α+β) = sin α cos β + cos α sin β
    sin (π/6) = 1/3 + cos α sin β
            1/2 = 1/3 + cos α sin β
cos α sin β = 1/2 - 1/3
cos α sin β = 3/6 - 2/6
cos α sin β = 1/6

=>  sin α-β = sin α cos β - cos α sin β
=>  sin α-β = 1/3 - 1/6
=>  sin α-β = 2/6 - 1/6
=>  sin α-β = 1/6