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If tan theta = (x sin phi)/(1-x cos phi)...

If `tan theta = (x sin phi)/(1-x cos phi)` and `tan phi =(y sin theta)/(1-y cos theta)` then the value of `x/y` is

Text Solution

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`tantheta-xcosphitantheta=xsinphi`
`x=tantheta/(sinphi+cosphitantheta`
`tanphi-ytanphicostheta=ysintheta`
`y=tanphi/(sintheta+costhetatanphi`
`x/y=(tantheta/(sinphi+cosphitantheta))/(tanphi/(sintheta+costhetatanphi))`
`x/y=(sintheta/sin(theta+phi))/(sinphi/sin(phi+theta))`
`x/y=sintheta/sinphi`.
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