Mathematics, 30.07.2019 04:10 xXCoryxKenshinXx
Rewrite the product 2sin(8x) cos(5x) as a sum or difference
Answers: 2
![\bf \textit{Product to Sum Identities} \\\\ sin(\alpha)sin(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad -\quad cos(\alpha+\beta)] \\\\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)] \\\\\\ sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)]\leftarrow \textit{let's use this one} \\\\\\ cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}](/tpl/images/0149/1841/9b2a9.png)
![\bf 2sin(8x)cos(5x)\implies ~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\left[ \cfrac{sin(8x+5x)+sin(8x-5x)}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill sin(13x)+sin(3x)~\hfill](/tpl/images/0149/1841/6f24c.png)
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