Question

8 sin 3x cos 3x >= 2sqrt3

Answer 1

$8sin3xcos3xgeq2sqrt3;\ 4cdot2sin3xcos3xgeq2sqrt3;\ 4cdotsin6xgeq2sqrt3;\ sin6xgeqfrac{2sqrt3}{4};\ sin6xgeqfrac{sqrt3}{2};\ frac{pi}{3}+2pi nleq6xleqfrac{2pi}{3}+2pi n, nin Z;\ frac{pi}{18}+frac{pi n}{3}leq xleqfrac{2pi}{18}+frac{pi n}{3}, nin Z;\\ xinleft[frac{pi}{18}+frac{pi n}{3};frac{pi}{9}+frac{pi n}{3}right], nin Z.$