Question

sin(2х +пи/3) +cos(2х + пи/3) =0

Answer 1

$sin(2x+ frac{pi}{3} )+cos(2x+ frac{pi}{3} )=0; |:cos(2x+frac{pi}{3})ne 0\\tg(2x+frac{pi}{3})+1=0\\tg(2x+frac{pi}{3})=-1\\2x+frac{pi}{3}=-frac{pi}{4}+pi n,; nin Z\\2x=-frac{pi}{3}-frac{pi}{4}+pi n,; nin Z\\2x=-frac{7pi} {3}+pi n,; nin Z\\x=-frac{7pi}{6}+frac{pi}{2}n,; nin Z$