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[latex]1.\quad 2cos(x+\frac{\pi}{3})-1=0\\\\cos(x+\frac{\pi}{3})=\frac{1}{2}\\\\x+\frac{\pi}{3}=(-1)^{n}\frac{\pi}{6}+\pi n\\\\x=(-1)^{n}\frac{\pi}{6}-\frac{\pi}{3}+\pi n,n\in Z\\\\3.\quad tg^2x+3tgx=-2\\\\t=tgx,\quad t^2+3t+2=0\\\\t_1=-2,t_2=-1\; (teor.\; Vieta)\\\\tgx=-2,\; x=-arctg2+\pi n,n\in Z\\\\tgx=-1,\; x=-\frac{\pi}{4}+\pi k,k\in Z[/latex]