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Question

Prove the following:
cos(π4x)cos(π4y)sin(π4x)sin(π4y)=sin(x+y)

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Solution

LHS=cos(π4x)cos(π4y)sin(π4x)sin(π4y)=cos(π4x+π4y)

Using identity cosAcosBsinAsinB=cos(A+B)

=cos(π2(x+y))=sin(x+y)=RHS

cos(π4x)cos(π4y)sin(π4x)sin(π4y)=sin(x+y)

Hence proved

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