Question

sin(2α+β)+2sinβ=0 求正:tanα=3tan(α+β)

Answer 1

sin(2α+β)+2sinβ=0

sin(α+α+β)+2sin(a+β-α)=0(配方)

sinacos(α+β)+cosasin(a+b)+2sin(α+β)cosa-2cos(α+β)sina=0(展开)

3cosasin(α+β)-sinacos(α+β)=0

3cosasin(α+β)=sinacos(α+β)

3cosasin(α+β)/cosacoa(α+β)=sinacos(α+β)/cosacoa(α+β)

tanα=3tan(α+β)