Prove that sin(α+β)+sin(α−β)=2sin(α)cos(β)\sin(\alpha + \beta) + \sin(\alpha - \beta) = 2\sin(\alpha)\cos(\beta)sin(α+β)+sin(α−β)=2sin(α)cos(β).
Use the double angle formula
Use the Law of Cosines
Use the Law of Sines
Use angle addition formulas and combine like terms