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Prove that:(sinx-siny)/(cosx+cosy)=tan(x...

Prove that:`(sinx-siny)/(cosx+cosy)``=tan``(x-y)/2`

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Verified by Experts

Here, we will use the formulas,
`sin A - sin B = 2sin((A-B)/2)cos((A+B)/2)`
`cos A + cos B = 2cos((A-B)/2)cos((A+B)/2)`
`L.H.S.=(sinx-siny)/(cosx+cosy)`
`=(2sin((x-y)/2)cos((x+y)/2))/(2cos((x-y)/2)cos((x+y)/2))`
`=sin((x-y)/2)/cos((x-y)/2)=tan((x-y)/2)=R.H.S.`
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