Answer
See below.
Work Step by Step
$LHS=cos(\alpha-\beta)cos(\alpha+\beta)=[cos(\alpha)cos(\beta)+sin(\alpha)sin(\beta)][cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta)]=cos^2(\alpha)cos^2(\beta)-sin^2(\alpha)sin^2(\beta)=cos^2(\alpha)(1-sin^2(\beta))-(1-cos^2(\alpha))sin^2(\beta)=cos^2(\alpha)-sin^2(\beta)=RHS$