Answer:

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Verified answer

Step-by-step explanation:

cos(

4

π

−x)cos(

4

π

−y)−sin(

4

π

−x)sin(

4

π

−x)

We know that, cos(A+B)=cosAcosB−sinAsinB

Here, A=

4

π

−x,B=

4

π

−y

A+B=

2

π

−(x+y)

cos(

4

π

−x)cos(

4

π

−y)−sin(

4

π

−x)sin(

4

π

−x)=cos(

2

π

−(x+y))=sin(x+y)