Question

$-tg(2x- frac{ pi}{6} )=1$

Answer 1

$-tg(2x-frac{pi}{6})=1\\tg(2x-frac{pi}{6})=-1\\2x-frac{pi}{6}=-frac{pi}{4}=pi n,; nin Z\\2x=frac{pi}{6}-frac{pi}{4}+pi n=-frac{pi}{12}+pi n,; nin Z\\x=-frac{pi}{24}+frac{pi n}{2}; ,; nin Z$