Irratsional tenglamalar va tengsizliklar mavzusidan test savollari

tg(x+\frac{\pi }{4})\ge 1 tengsizlikni yeching.

y=\sqrt{1+\log _{\frac{1}{2}}\cos x} funksiya x ning qanday qiymatlarida aniqlangan?

\sin ^{2}x-\frac{5}{2}\sin x+1>0 tengsizlik x(x\in \lbrack 0;2\pi \rbrack ) ning qanday qiymatlarida o‘rinli?

2\sin 2x-\tan ^{-1}\frac{\pi }{4} tengsizlikni yeching.

\cos ^{2}x-\frac{5}{2}\cos x+1>0 tengsizlik x (x\in \lbrack 0;2\pi \rbrack ) ning qanday qiymatlarida o‘rinli?

y=\sqrt{\log _{\frac{1}{2}}\sin x} funksiya x(x\in \lbrack 0;2\pi \rbrack ) ning qanday qiymatlarida aniqlangan?

\cos ^{2}x<\frac{\sqrt{2}}{2}+\sin ^{2}x tengsizlikni yeching.

y=\log _{2}\sin x funksiyaning aniqlanish sohasini toping.

y=\log _{5}(5\sin x) funksiyaning aniqlanish sohasini toping.

\sin x\cdot \cos x>\frac{\sqrt{2}}{4} tengsizlikni yeching.

y=\sqrt{tgx+1} funksiyaning aniqlanish sohasini toping.

1-2\cos 2x>\sin ^{2}2x tengsizlikni yeching.

\vert \sin x+1\vert >1.5 tengsizlik x ning (0;\pi ) kesmaga tegishli qanday qiymatlarida o‘rinli bo‘ladi?

y=\sqrt{lg(\cos x)} funksiyaning aniqlanish sohasiga tegishli nuqtalardan nechtasi \lbrack -10\pi ;10\pi \rbrack kesmaga tegishli?

\sin 5x\cos 4x+\cos 5x\sin 4x>\frac{1}{2} tengsizlikni yeching.

\cos 2x\le -\frac{1}{2} tengsizlikning \lbrack 0;2\pi \rbrack kesmadagi yechimini toping.

1-2\sin 4x<\cos ^{2}4x tengsizlikni yeching.

(\cos x+2)\vert x-5\vert (x-2)\le 0 tengsizlikni yeching.

\sin ^{2}3x-\cos ^{2}3x\le -\frac{\sqrt{3}}{2} tengsizlikni yeching.

2\sin x\ge \sqrt{2} tengsizlikni yeching.

\vert 1+\sin x\vert \le \frac{1}{2} tengsizlikning \lbrack 0;2\pi \rbrack oraliqdagi eng katta va eng kichik yechimlari ayirmasini toping.

4\cos ^{2}x-3\ge 0 tengsizlikni yeching.

(\pi -\varepsilon )^{\ln (\cos ^{4}x-\sin ^{4}x)}\ge 1 tengsizlikning \lbrack 0;\pi \rbrack oraliqqa tegishli barcha yechimlarini aniqlang.

\cos 5x\cos 4x+\sin 5x\sin 4x<\frac{\sqrt{3}}{2} tengsizlikni yeching.

\begin{cases}0\le x\le \pi\\2\cos ^{2}x-1\le \frac{1}{2}\end{cases} tengsizlikni yeching.

9^{\log _{3}(x-3)}>1 tengsizlikning eng kichik butun yechimini toping.

\begin{cases}0\le x\le \frac{\pi }{2}\\1\le tgx\le \sqrt{3}\end{cases} tengsizliklar sistemasining eng katta va eng kichik yechimlari ayirmasini toping.

-1-\frac{2}{\sqrt{3}}\cos x>0 tengsizlik \lbrack -\pi ;\pi \rbrack kesmada nechta butun yechimga ega?

\cos x<\sin x tengsizlikni yeching.

(\frac{\pi }{2}-\frac{e}{3})^{\ln (2\cos x)}\ge1 tengsizlikni yeching x\in \lbrack 0;2\pi \rbrack