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If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) , t...

If `(sin(x+y))/(sin(x-y))=(a+b)/(a-b)` , then show that `(tanx)/(tany)=(a)/(b)`.

Text Solution

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LHS `=(sin(x+y))/(sin(x-y))`
`(sinx cosy+cosx siny)/(sinx cosy-cosxsiny)`
`=(tanx+tany)/(tanx-tany)`
(Divide `N^( r)` and `D^( r)` by `cos xcos y`)
=RHS Hence proved.
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