Question

$tan( frac{pi}{3} - 4x ) = - 1$​

Answer 1

$sf displaystyle tg(frac{pi}{3}-4x)=-1\frac{pi}{3}-4x=- frac{pi}{4}+pi k, kin Z\-4x=-frac{pi}{4}-frac{pi}{3}+pi k,kin Z\\-4x=-frac{7pi}{12}+pi k,kin Z|:(-4)\x=frac{7}{48}-frac{pi k}{4},kin Z\\ boxed{x=frac{7}{48}-frac{pi k}{4},kin Z}$