# DISEQUAZIONI GONIOMETRICHE

 $\sqrt{3·{\mathrm{tan}}^{2}x-1}-\sqrt{3}·\mathrm{tan}x>0$. (R) $\frac{{\mathrm{sin}}^{2}\left(\pi -x\right)·\mathrm{cos}\left(\frac{\pi }{4}-x\right)}{\mathrm{tan}x-1}<0$. (R) $\sqrt{1+{\mathrm{sin}}^{2}}x<1-\mathrm{sin}x$. (R) $\frac{\mathrm{cos}x}{1+\mathrm{sin}x}+\mathrm{tan}x>2$ . (R) $\sqrt{\mathrm{cot}x}\le \mathrm{cot}x-1$. (R) $\mid \sqrt{3}·{\mathrm{tg}}^{2}x-2·\mathrm{tgx}\mid <\sqrt{3}$. (R) $\frac{2·\mid \mathrm{sin}x\mid -1}{2·\mathrm{sin}x-1}>0$. (R) $\frac{2·\mathrm{sin}\left(2x+\frac{\pi }{3}\right)-1}{\mathrm{sin}x+\mathrm{cos}x}\le 0$ . (R) $\frac{2-\sqrt{3}·\mathrm{sin}x-\mathrm{cos}x}{2·\mathrm{cos}x+\sqrt{3}}\ge 0.$ (R) $\frac{\mathrm{cos}x}{1+\mathrm{sin}x}+\mathrm{tgx}>2$ . (R) $\frac{\mathrm{sin}\left(x+\frac{\pi }{3}\right)+\mathrm{cos}\left(x+\frac{\pi }{3}\right)-1}{{\mathrm{cot}}^{3}x+1}\ge 0$ . (R) $2·\mathrm{cos}\left(2x-\frac{\pi }{4}\right)-\sqrt{2}<0$ (R) $\left(4·\mathrm{cos}x-\sqrt{5}-1\right)·\left(\mathrm{tan}x-\sqrt{2}+1\right)>0$ (R) $\sqrt{2\mid \mathrm{cos}x\mid }-1\le 0$ (R) $\sqrt{3-4·{\mathrm{cos}}^{2}x}>3·\mathrm{sin}x+1$ (R) $\sqrt{4{\mathrm{sin}}^{2}x+3}>2\mathrm{sin}x+1$ (R) $\frac{\mathrm{cos}x-\mathrm{sin}x-1}{\mathrm{cos}\left(x-\frac{\pi }{3}\right)}\le 0$ (R) $\frac{1-2\mathrm{sin}x}{\mathrm{cos}x}\le 0$ (R) ${\mathrm{cos}}^{2}x-2\sqrt{3}·\mathrm{sin}x·\mathrm{cos}x-{\mathrm{sin}}^{2}x>0$ (R) $\mathrm{cos}\left(x+\frac{\pi }{6}\right)+\left(\sqrt{3}+2\right)\mathrm{sin}\left(x+\frac{\pi }{6}\right)+1>0$ (R) $1-\sqrt{2}·\mathrm{cos}\left(x+\frac{\pi }{6}\right)\le 0$ (R) $2·{\mathrm{sin}}^{2}x<\left(2+\sqrt{2}\right)·\mathrm{sin}x-\sqrt{2}$ (R) $\frac{2·{\mathrm{sin}}^{2}x-1}{\mathrm{cos}x}\le 0$ (R) $\sqrt{1+2·\mathrm{cos}x}>1-\mathrm{cos}x$ (R) $\sqrt{3}·\mathrm{cot}\left(\frac{x}{2}\right)\ge 3$ (R) $4·{\mathrm{cos}}^{2}x-4·\mathrm{cos}x-4>-5$ (R) $\left(1-2·\mathrm{sin}x\right)·\left(2·\mathrm{cos}x+\sqrt{3}\right)\le 0$(R) $\mid {\mathrm{tan}}^{2}x-1\mid -2·{\mathrm{tan}}^{2}x<0$ (R) $2·\mathrm{sin}2x-\sqrt{3}<0$ (R) ${\mathrm{tan}}^{2}x<\left(1+\sqrt{3}\right)·\mathrm{tan}x-\sqrt{3}$(R) $\left(2·\mathrm{cos}x-1\right)·\left({\mathrm{cos}}^{2}x-1\right)\le 0$ (R) $2·\mathrm{tan}x+\sqrt{{\mathrm{tan}}^{2}x-1}\le 1-\mathrm{tan}x$ (R) $\mathrm{tan}\frac{x}{2}+1>0$ (R) $2·{\mathrm{cos}}^{2}x-7·\mathrm{cos}x+3<0$ (R) $\frac{2\sqrt{2}\mathrm{sin}x-\sqrt{6}}{3·{\mathrm{tan}}^{2}x-1}\le 0$ (R) $\frac{2·\mid \mathrm{cos}x\mid -1}{2·\mathrm{tan}x}>0$ (R) $2·\mathrm{cos}2x-1\le 0$ (R) $3·{\mathrm{tan}}^{2}x-\left(3+\sqrt{3}\right)·\mathrm{tan}x+\sqrt{3}<0$ (R) $\left(2·\mathrm{sin}x-\sqrt{3}\right)·\left(2·\mathrm{cos}x+\sqrt{2}\right)\le 0$ (R) $\sqrt{3-4·{\mathrm{cos}}^{2}x}<1+3·\mathrm{sin}x$ (R) $\mathrm{sin}\left(x-\frac{\pi }{4}\right)\le 1$ (R) $3·\mathrm{sin}x-\sqrt{3}·\mathrm{cos}x>0$ (R) $\left(3·{\mathrm{tan}}^{2}x-1\right)·\left(\mathrm{sin}x+1\right)\ge 0$ (R) $\frac{1-2·\mid \mathrm{sin}x\mid }{2·\mathrm{sin}x+1}>0$ (R) $\mathrm{cos}\left(x+\frac{\pi }{3}\right)\ge \frac{1}{2}$(R) $\mathrm{sin}x-\sqrt{3}·\mathrm{cos}x>0$ (R) $\frac{{\mathrm{tan}}^{2}-1}{2·\mathrm{sin}x+1}\le 0$ (R) $\sqrt{{\mathrm{cot}}^{2}x-1}<\mathrm{cot}x+1$ (R) $\mathrm{sin}\frac{x}{2}\le \frac{\sqrt{2}}{2}$(R) ${\mathrm{tan}}^{2}x<2·\mathrm{tan}x-2·\sqrt{3}+3$ (R) $\left(\mathrm{cot}x-1\right)·\left(2·\mathrm{sin}x+1\right)\ge 0$ (R) $\frac{\mid \mathrm{sin}x\mid }{2·\mathrm{cos}x-1}\ge 0$ (R) $2·\mathrm{tan}x+\sqrt{{\mathrm{tan}}^{2}x-1}\le 1+\mathrm{tan}x$ (R)