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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 $\frac32$?

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    $\begingroup$ Don't forget that $-\cos x = -1\cdot \cos x$, so $$1/2 \cos x (3 + y) - \cos x = \cos x(3/2 + y/2 - 1) = \cos x(1/2 + y/2)$$ $\endgroup$ – Ilya Jul 21 '14 at 18:31
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\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*}

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