[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]
