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If tanx/tany=(1+cos^2x)/(1+sin^2x), show...

If `tanx/tany=(1+cos^2x)/(1+sin^2x)`, show that `sin(3x+y)=7sin(x-y)`

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`tanx/tany=(1+cos^2x)/(1+sin^2x)`
`(tanx-tany)/(tanx+tany)=(cos^2x-sin^2x)/3`
`sin(x-y)/sin(x+y)=(cos2x)/3`
`3sin(x-y)=sin(x-y)cos(2x)`
`6sin(x-y)=sin(3x+y)+sin(y-x)`
`6sin(x-y)=sin(3x+y)-sin(x-y)`
`sin(3x+y)=7sin(x-y)`.
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