Dik :

Karena sudut lancip, maka :

tan α = 1 —> sin α = cos α = ½√2
tan β = 1/3 —> sin β = (√10) /10 dan cos β = (3√10) /10
sin (α – β) = sin α cos β – cos α sin β
sin (α – β) = {½√2 . (3√10) /10} – {½√2 . (√10) /10}
sin (α – β) = {(3√20) /20} – {(√20) /20}
sin (α – β) = (3√20 – √20) /20
sin (α – β) = (2√20) /20
sin (α – β) = {2√(4.5)} /20
sin (α – β) = (4√5) /20
sin (α – β) = (4/20)√5
sin (α – β) = 1/5√5 <—— Jawaban