sin(α+β) = sinα cosβ + cosα sinβ となる理由

sin(α+β)
= cos((α+β)-π/2)
= cos((α-π/2)+β)
= cos(α-π/2)cosβ - sin( α-π/2    )sinβ
= cos(α-π/2)cosβ + sin((α-π/2)+π)sinβ
= cos(α-π/2)cosβ + sin( α+π/2    )sinβ
= sin α      cosβ + cos  α          sinβ