Question

化简sin(α+β)cos(γ-β)-cos(β+α)sin(β+γ)

sin(α+β)cos(γ-β)-cos(β+α)sin(β+γ)

Answer 1

你要画到什么程度啊？
sin(α+β)cos(γ-β)-cos(β+α)sin(β+γ)
=[sin(α+γ)+sin(α+2β-γ)]/2-[sin(α+2β+γ)+sin(α-γ)]/2
=[sin(α+γ)-sin(α-γ)+sin(α+2β-γ)-sin(α+2β+γ)]/2
=[2sinαcosγ+2cos(α+2β)sinγ]/2
=sinαcosγ+cos(α+2β)sinγ

Answer 2

sin(α+β)cos(γ-β)-cos(β+α)sin(β-γ)
=sin(α+β)cos(γ-β)+cos(α+β)sin(γ-β)
=sin[(α+β)+(γ-β)]
=sin(α+γ)

Answer 3

sin(α+β)cos(γ-β)-cos(β+α)sin(β+γ)