Sin (arcsin (3/5) + arcsin (8/17)) = ?

Как решить

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