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Prove that: (cosx+cosy)^2+(sinx-siny)^2=...

Prove that: `(cosx+cosy)^2+(sinx-siny)^2``=4cos^2``(x+y)/2`

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Given,
L.H.S
`(cosx+cosy)^2+(sinx−siny)^2`
`=(cos^2x+cos^2y+2cosxcosy)+(sin^2x+sin^2y−2sinxsiny)`
...
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