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

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

Text Solution

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LHS = `(sinx-siny)/(cosx+cosy)`
`=(2cos(x+y)/(2)sin(x-y)/(2))/(2cos(x+y)/(2)cos(x-y)/(2))=(sin(x-y)/(2))/(cos(x-y)/(2))`
`=tan(x-y)/(2)`= RHS Hence Proved.
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