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Prove that `(sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)`

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Prove that `(sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)`
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`L.H.S. = (sin(x+y))/(sin(x-y))`
`=(sinxcosy+sinycosx)/(sinxcosy-cosxsiny)`
Dividing numerator and denominator by `cosxcosy`
`=((sinx/cosx)+(siny/cosy))/((sinx/cosx)-(siny/cosy))`
`=(tanx+tany)/(tanx-tany)=R.H.S`
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