# How do you prove 2sin((5pi)/6)cos(pi/6)=sin120?

$2 \sin \left(\frac{5 \pi}{6}\right) \cos \left(\frac{\pi}{6}\right) = 2 \sin \left(\pi - \frac{\pi}{6}\right) \cos \left(\frac{\pi}{6}\right) = 2 \sin \left(\frac{\pi}{6}\right) \cos \left(\frac{\pi}{6}\right) = \sin 2 \cdot \left(\frac{\pi}{6}\right) = \sin 60 = \sin \left(180 - 60\right) = \sin 120$[Proved]