Sin(arcsin(3/5)+arcsin(8/17))=77/85
Обозначим α = arcsin(3/5) и β = arcsin(8/17)
sin α = 3/5; cos α = √(1 - 9/25) = √(16/25) =4/5
sin β = 8/17; cosβ = √(1 - 64/289) = √(225/289) =15/17
Sin(arcsin(3/5)+arcsin(8/17)) = sin (α + β) = sinα · cosβ + sinβ · cosα =
= 3/5 · 15/17 + 8/17 · 4/5 = 9/17 + 32/(17·5) = 45/85 + 32/85 = 77/85
Ответ: 77/85