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Prove the following `cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)`

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Prove the following `cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)`
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`L.H.S. = cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)`
We know, `cosAcosB-sinAsinB = cos(A+B)`,
`:. cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y) = cos(pi/4-x+pi/4-y)`
`=cos(pi/2-(x+y))`
`=sin(x+y) = R.H.S.`
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