Find that sin(n+1)*sin(n+2)x+ cos(n+1)x*cos(n+2)x.
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sin(n+1)x*sin(n+2)*x+cos(n+1)x*cos(n+2)x
=cos{(n+1)*x-(n+2)*x}
=cos{nx+x-nx-2x}
=cos(-2x)
=cos 2x
=cos{(n+1)*x-(n+2)*x}
=cos{nx+x-nx-2x}
=cos(-2x)
=cos 2x
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