We recognise this expression as the right hand side of:

cos(

α−β) = cosαcosβ+ cosαcosβ,

with *α* = *x *+* y* and *β* = *y.*

We can now write this in terms of cos(*α* − *β*) as follows:

cos(*x* + *y*)cos *y* + sin(*x* + *y*)sin *y*

= cos[(

x+y) − (y)]= cos

x

We have reduced the expression to a single term.

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