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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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LHS `=(cosx+cosy)^(2)+(sinx-siny)^(2)`
`=[2cos(x+y)/(2)cos(x-y)/(2)]^(2)`
`=4cos^(2)(x+y)/(2)cos^(2)(x-y)/(2)+4cos^(2)(x+y)/(2)sin^(2)(x-y)/(2)`
`=4cos^(2)(x+y)/(2)[cos^(2)(x-y)/(2)+sin^(2)(x-y)/(2)]`
`4cos^(2)(x+y)/(2)(1)=[4cos^(2)(x+y)/(2)sin^(2)(x-y)/(2)+sini^(2)(x-y)/(2)]`
`=4cos^(2)(x+y)/(2)(1)=4cos^(2)(x+y)/(2)`= RHS Hence proved.
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