Question

sqrt{3} tg(frac{pi}{3}-x)-1leq 0

Answer 1

$displaystyle sqrt{3} tg(frac{pi}{3}-x)-1leq 0\\tg( frac{ pi }{3}-x) leq frac{1}{ sqrt{3}}\\ * - frac{ pi }{2} textless frac{ pi }{3}-x leq frac{ pi }{6}; (+2 pi n; nin Z)\\ **frac{ pi }{2} textless frac{ pi }{3}-x leq frac{7 pi }{6}; (+2 pi n; nin Z)\\ * - frac{ pi }{2}- frac{ pi }{3} textless -x leq frac{ pi }{6}- frac{ pi }{3}; (+2 pi n; nin Z)\\ ** frac{ pi }{2}- frac{ pi }{3} textless -x leq frac{7 pi }{6}- frac{ pi }{3}; (+2 pi n; nin Z)$

$displaystyle * frac{ pi }{6}+2 pi n leq x textless frac{5 pi }{6}+2 pi n; nin Z\\ ** - frac{5 pi }{6} leq x textless - frac{ pi }{6}+2 pi n; nin Z$