Question

Докажите тождество sin (α+β) + sin (α-β) = 2 sin α cos β

Answer 1

sin(α+β) = sin(α)∙cos(β) + cos(α)∙sin(β)
sin(α-β) = sin(α)∙cos(β) - cos(α)∙sin(β)
sin(α+β) + sin(α-β) = (sin(α)∙cos(β) + cos(α)∙sin(β)) + (sin(α)∙cos(β) - cos(α)∙sin(β))
sin(α+β) - sin(α-β) = 2∙sin(α)∙cos(β)