Trigonometric expression manipulation I'm working on manipulating trig expressions using Khan Academy.

According to the provided answer this:

$$\cos(\theta)\sin(\theta)$$

is supposed to equal: 

$$\frac1 2\sin(2\theta)$$

I do not understand how, so could someone please show me.

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Hint: $\sin (x + y) =\sin (x) \cdot \cos (y) +\cos (x) \cdot \sin (y) $

What happens when $x=y$ ?
$(e^{ia})^2    =  e^{2ia}.$

L.H.S   =  $( cos^2(a)   - sin^2(a) , 2sin(a).cos(a))$

R.H.S  =   $(cos(2a) , sin(2a))$