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[latex]2cos^22x+sin2x-1\ \textless \ 0\\\\2(1-sin^22x)+sin2x-1\ \textless \ 0\\\\-2sin^22x+sin2x+1\ \textless \ 0\\\\t=sin2x\; ,\; \; 2t^2-t-1\ \textgreater \ 0\; ,\; \; -1 \leq t \leq 1\\\\D=9\; ,\; \; t_1=\frac{1-3}{4}=-\frac{1}{2}\; ,\; \; t_2=\frac{1+3}{4}=1\\\\+++(-\frac{1}{2})---(1)+++\\\\t\in (-\infty ,-\frac{1}{2})\cup (1,+\infty )\; \; \; \Rightarrow \; \; \; \left \{ {{sin2x\ \textless \ -\frac{1}{2}} \atop {sin2x\ \textgreater \ 1}} \right. \\\\-1 \leq sin2x \leq 1\; \; \; \Rightarrow \; \; \; sin2x\ \textless \ -\frac{1}{2}\\\\-\frac{5\pi }{6}+2\pi n\ \textless \ 2x\ \textless \ -\frac{\pi}{6}+2\pi n\; ,\; n\in Z[/latex]
[latex]-\frac{5\pi}{12}+\pi n \leq x \leq -\frac{\pi}{12}+\pi n\; ,\; n\in Z\\\\Otvet:\; \; A)\; x\in (-\frac{5\pi}{12}+\pi n\; ;\; -\frac{\pi}{12}+\pi n)\; ,\; n\in Z[/latex]
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