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

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

Text Solution

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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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Knowledge Check

If (sinx)/(siny)=pand(cosx)/(cosy)=q , then x = ?

A

A) Rs. 1250

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B) Rs. 600

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D) Rs. 1500

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