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Решите неравенство. \(2+\frac{9}{cos x}\leq \frac{5}{cos^{2} x}\)

Решение №32659: \( \left [\frac{\pi}{3}+2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right )\cup\left (\frac{3\pi}{2}+2\pi n; \frac{5\pi}{3}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [\frac{\pi}{3}+2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right )\cup\left (\frac{3\pi}{2}+2\pi n; \frac{5\pi}{3}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство. \(6+\frac{4}{cos^{2} x}\geq \frac{11}{cos x}\)

Решение №32660: \( \left [\frac{\pi}{3}+2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right )\cup\left (\frac{3\pi}{2}+2\pi n; \frac{5\pi}{3}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [\frac{\pi}{3}+2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right )\cup\left (\frac{3\pi}{2}+2\pi n; \frac{5\pi}{3}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство. \(\frac{3}{sin^{2} x}+ \frac{4}{sin x}-4\geq 0\)

Решение №32661: \( \left [-\frac{\pi}{6}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \pi+2\pi n\right )\cup\left (\pi+2\pi n; \frac{7\pi}{6}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{6}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \pi+2\pi n\right )\cup\left (\pi+2\pi n; \frac{7\pi}{6}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство. \(\frac{5}{sin^{2} x}+\frac{7}{sin x}-6\geq 0\)

Решение №32662: \( \left [-\frac{\pi}{6}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \pi+2\pi n\right )\cup\left (\pi+2\pi n; \frac{7\pi}{6}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{6}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \pi+2\pi n\right )\cup\left (\pi+2\pi n; \frac{7\pi}{6}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\( \frac{1}{cos^{2} x} + \frac{3}{sin( \frac{\pi}{2}+ x)} +2\geq 0 \)

Решение №32663: \( \left [-\frac{2\pi}{3}+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (-\frac{\pi}{2}+2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{2\pi}{3}+2\pi n\right ]\cup\left {\pi+2\pi n\right }, n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{2\pi}{3}+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (-\frac{\pi}{2}+2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{2\pi}{3}+2\pi n\right ]\cup\left {\pi+2\pi n\right }, n \in \mathbb{Z}\)

Решите неравенство.\(\frac{1}{sin^{2} x-\frac{3}{cos \left (\frac{3\pi}{2}+ x}\right)+2\geq 0\)

Решение №32664: \( \left [-\frac{7\pi}{6}+2\pi n; -\pi+2\pi n\right )\cup\left (-\pi+2\pi n; 2\pi n\right )\cup\left (2\pi n; \frac{\pi}{6}+2\pi n\right ]\cup\left {\frac{\pi}{2}+2\pi n\right }, n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{7\pi}{6}+2\pi n; -\pi+2\pi n\right )\cup\left (-\pi+2\pi n; 2\pi n\right )\cup\left (2\pi n; \frac{\pi}{6}+2\pi n\right ]\cup\left {\frac{\pi}{2}+2\pi n\right }, n \in \mathbb{Z}\)

Решите неравенство.\(7tg^{2} x-\frac{1}{cos x}+1\geq 0\)

Решение №32665: \( \left (-\frac{\pi}{2}+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (-\frac{\pi}{2}+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(6tg^{2} x-\frac{1}{cos x}+1\geq 0\)

Решение №32666: \( \left (-\frac{\pi}{2}+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (-\frac{\pi}{2}+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \frac{3\pi}{2}+2\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(\frac{1}{tg^{2} x}-\frac{1}{sin x}-1>0\)

Решение №32667: \( \left (-\frac{7\pi}{6}+2\pi n; -\pi+2\pi n\right )\cup\left (-\pi+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (-\frac{\pi}{2}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \frac{\pi}{6}+2\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (-\frac{7\pi}{6}+2\pi n; -\pi+2\pi n\right )\cup\left (-\pi+2\pi n; -\frac{\pi}{2}+2\pi n\right )\cup\left (-\frac{\pi}{2}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \frac{\pi}{6}+2\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(\frac{1}{tg^{2} x}+\frac{3}{sin x}+3>0\)

Решение №32668: \( \left (-\frac{\pi}{6}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \pi+2\pi n\right )\cup\left (\pi+2\pi n; \frac{7\pi}{6}+2\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (-\frac{\pi}{6}+2\pi n; 2\pi n\right )\cup\left (2\pi n; \frac{\pi}{2}+2\pi n\right )\cup\left (\frac{\pi}{2}+2\pi n; \pi+2\pi n\right )\cup\left (\pi+2\pi n; \frac{7\pi}{6}+2\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(sin^{2} x\leq 2sin x\)

Решение №32669: \( \left [2\pi n; \pi+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [2\pi n; \pi+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(cos^{2} x\leq 3cos x\)

Решение №32670: \( \left [-\frac{\pi}{2}+2\pi n; \frac{\pi}{2}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{2}+2\pi n; \frac{\pi}{2}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(8sin^{4} x-6sin^{2} x+1\geq 0\)

Решение №32671: \( \left [-\frac{\pi}{6}+\pi n; \frac{\pi}{6}+\pi n\right ]\cup\left [\frac{\pi}{4}+\pi n; \frac{3\pi}{4}+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{6}+\pi n; \frac{\pi}{6}+\pi n\right ]\cup\left [\frac{\pi}{4}+\pi n; \frac{3\pi}{4}+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(8sin^{4} x-10sin^{2} x+3\geq 0\)

Решение №32672: \( \left [-\frac{\pi}{4}+\pi n; \frac{\pi}{4}+\pi n\right ]\cup\left [\frac{\pi}{3}+\pi n; \frac{2\pi}{3}+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{4}+\pi n; \frac{\pi}{4}+\pi n\right ]\cup\left [\frac{\pi}{3}+\pi n; \frac{2\pi}{3}+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(8cos^{4} x-18cos^{2} x+9\leq 0\)

Решение №32673: \( \left [-\frac{\pi}{6}+2\pi n; \frac{\pi}{6}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{6}+2\pi n; \frac{\pi}{6}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(8cos^{4} x-22cos^{2} x+5\leq 0\)

Решение №32674: \( \left [-\frac{\pi}{3}+2\pi n; \frac{\pi}{3}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{3}+2\pi n; \frac{\pi}{3}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(3tg^{4} x-4tg^{2} x+1\geq 0\)

Решение №32675: \( \left [-\frac{\pi}{6}+\pi n; \frac{\pi}{6}+\pi n\right ]\cup \left [\frac{\pi}{4}+\pi n; \frac{\pi}{2}+\pi n\right )\cup \left (\frac{\pi}{2}+\pi n; \frac{3\pi}{4}+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{6}+\pi n; \frac{\pi}{6}+\pi n\right ]\cup \left [\frac{\pi}{4}+\pi n; \frac{\pi}{2}+\pi n\right )\cup \left (\frac{\pi}{2}+\pi n; \frac{3\pi}{4}+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(3tg^{4} x-10tg^{2} x+3\geq 0\)

Решение №32676: \( \left [-\frac{\pi}{6}+\pi n; \frac{\pi}{6}+\pi n\right ]\cup \left [\frac{\pi}{3}+\pi n; \frac{\pi}{2}+\pi n\right )\cup \left (\frac{\pi}{2}+\pi n; \frac{2\pi}{4}+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{6}+\pi n; \frac{\pi}{6}+\pi n\right ]\cup \left [\frac{\pi}{3}+\pi n; \frac{\pi}{2}+\pi n\right )\cup \left (\frac{\pi}{2}+\pi n; \frac{2\pi}{4}+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(ctg^{4} x-5ctg^{2} x+4\leq 0\)

Решение №32677: \( \left [arcctg 2+\pi n; \frac{\pi}{4}+\pi n\right ]\cup \left [\frac{3\pi}{4}+\pi n; \pi-arcctg 2+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [arcctg 2+\pi n; \frac{\pi}{4}+\pi n\right ]\cup \left [\frac{3\pi}{4}+\pi n; \pi-arcctg 2+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(ctg^{4} x-10ctg^{2} x+9\leq 0\)

Решение №32678: \( \left [arcctg 3+\pi n; \frac{\pi}{4}+\pi n\right ]\cup \left [\frac{3\pi}{4}+\pi n; \pi-arcctg 3+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [arcctg 3+\pi n; \frac{\pi}{4}+\pi n\right ]\cup \left [\frac{3\pi}{4}+\pi n; \pi-arcctg 3+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(sin^{2} x>sin x\cdot cos x\)

Решение №32679: \( \left (\frac{\pi}{4}+\pi n; \pi+\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (\frac{\pi}{4}+\pi n; \pi+\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(cos^{2} x>sin x\cdot cos x\)

Решение №32680: \( \left (-\frac{\pi}{2}+\pi n; \frac{\pi}{4}+\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (-\frac{\pi}{2}+\pi n; \frac{\pi}{4}+\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(sin^{2} x-3sin x cos x-4cos^{2} x\leq 0\)

Решение №32681: \( \left [-\frac{\pi}{4}+\pi n; arctg 4+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{4}+\pi n; arctg 4+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(sin^{2} x-5sin x cos x-6cos^{2} x\leq 0\)

Решение №32682: \( \left [-\frac{\pi}{4}+\pi n; arctg 6+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{4}+\pi n; arctg 6+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(sin^{2} x-5sin x cos x+6cos^{2} x\geq 0\)

Решение №32683: \( \left [arctg 3+\pi n; arctg 2+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [arctg 3+\pi n; arctg 2+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(sin^{2} x-7sin x cos x+12cos^{2} x\geq 0\)

Решение №32684: \( \left [arctg 4+\pi n; arctg 3+\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [arctg 4+\pi n; arctg 3+\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(4sin^{2} x-9sin x cos x+11cos^{2} x<3\)

Решение №32685: \( \left (\frac{\pi}{4}+\pi n; arctg 8+\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (\frac{\pi}{4}+\pi n; arctg 8+\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(3sin^{2} x-8sin x cos x+9cos^{2} x<2\)

Решение №32686: \( \left (\frac{\pi}{4}+\pi n; arctg 7+\pi n\right ), n \in \mathbb{Z}\)

Ответ: \( \left (\frac{\pi}{4}+\pi n; arctg 7+\pi n\right ), n \in \mathbb{Z}\)

Решите неравенство.\(0,4sin x cos x+1\leq sin x+cos x\)

Решение №32687: \( \left [2\pi n; \frac{\pi}{2}+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [2\pi n; \frac{\pi}{2}+2\pi n\right ], n \in \mathbb{Z}\)

Решите неравенство.\(0,5sin x cos x+1\leq sin x+cos x+1\)

Решение №32688: \( \left [-\frac{\pi}{2}+2\pi n; \pi+2\pi n\right ], n \in \mathbb{Z}\)

Ответ: \( \left [-\frac{\pi}{2}+2\pi n; \pi+2\pi n\right ], n \in \mathbb{Z}\)