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Question

Prove the following:
cos(3π4+x)cos(3π4x)=2sinx

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Solution

LHS=cos(3π4+x)cos(3π4x)

=cos(3π4)cosxsin(3π4)sinx[cos(3π4)cosx+sin(3π4)sinx]

=2sin(3π4)sinx=2sinx=RHS

L.H.S=R.H.S

cos(3π4+x)cos(3π4x)=2sinx

Hence, proved

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