Question

Найдите значение выражения: sin(arctg 8/15 - arcsin8/15)

Answer 1

arctg 8/15 = α,   arcsin 8/15 = β
tgα = 8/15 
c = √(15² +8²) = 17 ⇒sinα = 8/17,   cosα = 15/17
sin β = 8/15
c = √(15² - 8²) = √161  ⇒cosβ = √161/15
sin (arctg 8/15 - arcsin 8/15) = sin (α - β) = sinα·cosβ - cosα·sinβ = 
= 8/17·√161/15-15/17·8/15 = 8/17·((√161 - 15)/15) = 8·(√161 - 15)/255