Can you show me where the "1/2" comes from? I'm struggling with a math assignment:
$$\frac12 \cos(x)·(3+2\sin(2x))−\cos(x)=0 ⇔ \cos(x)\left(\color{red}{\frac12}+\sin(2x)\right)=0$$ 
According to my knowledge it needs to be:
$$\frac12 \cos(x)·(3+2\sin(2x))−\cos(x)=0 ⇔ \cos(x)\left(\color{red}{\frac32}+\sin(2x)\right)=0$$ 
But why is it $\frac12$ and not $\frac32$?

\begin{align*}
\frac{1}{2} \cos(x)( 3 + 2 \sin(2x)) - \cos(x)
&= \color{blue}{\frac{3}{2} \cos(x)} + \cos(x) \sin (2x) \color{blue}{-\cos(x)} \\
&= \color{blue}{\frac{1}{2} \cos(x)} + \cos(x) \sin (2x) \\
&= \cos(x)(\frac{1}{2} + \sin(2x))
\end{align*}
