How to prove that $\sin(\theta)= 2\sin(\theta/2)\cos(\theta/2)$? $$\sin (\theta) = 2 \sin \left(\frac{\theta}{2}\right) \cos \left(\frac{\theta}{2}\right)$$
How? Please help. Thanks in advance.

If you know complex numbers, you can also use:
$e^{i\theta} = \cos(\theta)+i\sin(\theta)$ with $e^{i\theta} = (e^{i\frac{\theta}{2}})^2$ (this "trick" yields De Moivre's formula). 
Look at the imaginary part of that expression.
