5sina=3sin(a-2β)求证tan(a-β)+4tanβ=0

5sina=3sin(a-2β)求证tan(a-β)+4tanβ=0

答:
5sinα=3sin(α-2β)
5sin[(α-β)+β]=3sin[(α-β)-β]
5sin(α-β)coaβ+5cos(α-β)sinβ=3sin(α-β)cosβ-3cos(α-β)sinβ
2sin(α-β)cosβ=-8cos(α-β)sinβ
两边同除以cos(α-β)cosβ,
2tan(α-β)=-8tanβ
tan(α-β)+4tanβ=0.