# 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 $\frac32$?

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