Решите неравенство \(\cos{2x}\tg{x}>0.\) Укажите решение неравенства на промежутке \([-\frac{\pi}{2};\frac{3\pi}{2}].\) \((-\frac{\pi}{2};-\frac{\pi}{4})\cup(0;\frac{\pi}{4})\cup(\frac{\pi}{2};\frac{3\pi}{4})\cup(\pi;\frac{5\pi}{4})\) \((0;\frac{\pi}{4})\cup(\pi;\frac{5\pi}{4})\) \([-\frac{\pi}{2};-\frac{\pi}{4})\cup[0;\frac{\pi}{4})\cup[\frac{\pi}{2};\frac{3\pi}{4})\cup[\pi;\frac{5\pi}{4})\) \([0;\frac{\pi}{4})\cup[\pi;\frac{5\pi}{4})\)

Задание

Решите неравенство \(\cos{2x}\tg{x}\gt 0.\) Укажите решение неравенства на промежутке \([-\frac{\pi}{2};\frac{3\pi}{2}].\)

\((-\frac{\pi}{2};-\frac{\pi}{4})\cup(0;\frac{\pi}{4})\cup(\frac{\pi}{2};\frac{3\pi}{4})\cup(\pi;\frac{5\pi}{4})\)
\((0;\frac{\pi}{4})\cup(\pi;\frac{5\pi}{4})\)
\([-\frac{\pi}{2};-\frac{\pi}{4})\cup[0;\frac{\pi}{4})\cup[\frac{\pi}{2};\frac{3\pi}{4})\cup[\pi;\frac{5\pi}{4})\)
\([0;\frac{\pi}{4})\cup[\pi;\frac{5\pi}{4})\)