max0≤x≤π(16sin(x2)cos3(x2))\max_{0\le x\le \pi}\left(16\sin\left(\dfrac{x}{2}\right)\cos^{3}\left(\dfrac{x}{2}\right)\right)max0≤x≤π(16sin(2x)cos3(2x)) is equal to :
332\dfrac{3\sqrt{3}}{2}233
333\sqrt{3}33
434\sqrt{3}43
636\sqrt{3}63