Trig identity $\sin(x)\cos(x) = \sin(2x)/2$?

Question

http://tutorial.math.lamar.edu/Classes/CalcIII/TICylindricalCoords_files/eq0014MP.gif

Could someone tell me how $\sin(2x)$ arrives?

I know that there is a trig identity that says $2\cos(x)\sin(x) = \sin(2x)$ ... but this isn't isn't the case here... so could someone explain why?

Answer 1

Notice that:

$$\sin(a+b)=\sin a\cos b+\sin b\cos a$$

Since $2x = x+x$ we have:

$$\sin(2x)=\sin(x+x)=\sin x\cos x+\sin x\cos x=2\sin x\cos x$$

Now this simplifies to $\sin x\cos x = \sin(2x)/2$ as you want.