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Trigonometrik tengsizliklarni yechish

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10.08.2023

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Trigonometrik 
tengsizliklarni  yechish cos x ≥ a 
cos x ≤ a 
|a| ≤ 1Trigonometrik tengsizliklarni yechishning umumiy hollari
-   arccos a + 2 ?????? n ≤ x ≤ arccos a + 2 ?????? n
arccos a + 2 ?????? n ≤ x ≤ 2 ??????  - arccos a + 2 ?????? n Xususiy   hollarda
cos x ≥ 0 
cos x ≤ 0 
- /2 + ?????? 2 ?????? n ≤ x ≤  /2	??????  + 2 ?????? n
?????? /2 +  2 ?????? n ≤ x ≤  3 /2	
??????  + 2 ?????? n Xususiy   hollarda ( а = -1  uchun  )
1)  cos x ≥  1  
2)  cos x >  1  
1) X =  2?????? n
2) yechimi yo'q 1)  cos x ≤  1  
2 )  cos x <  1  
1) X €   R
2) X €   R , кроме  2	
?????? n  Xususiy  hollarda :
a > 1   (a < - 1) 
cos x ≥ a  cos x ≤ a 
Yechimi   yo’q
(Х €  R ) Х €  R
(yechimi yo’q ) Trigonometrik tengsizliklarni yechishning umumiy 
ko’rinishi
sin x ≥ a  sin x ≤ a 
arcsin a + 2 ?????? n ≤ x ≤  ??????  – arcsin a + 2 ?????? n
 – ?????? arcsin a + 2 ?????? n ≤ x ≤  2	??????   +  arcsin a + 2 ?????? n|a| ≤ 1 Xususiy hollarda
sin x ≥  0   sin x ≤  0  
2 ?????? n ≤ x ≤  ??????  + 2 ?????? n
 ?????? +  2 ?????? n ≤ x ≤  2	??????  + 2 ?????? n Xususiy   hollarda ( а = -1  uchun  )
1)  sin x ≥  1   1)  sin x ≤  1  
2)  sin x >  1   2 )  sin x <  1  
1) X =  /2 + 2?????? ?????? n
2) Yechimi yo’q 1) X €   R
2) X €   R ,  /2 + 2	
?????? ?????? n(undan 
tashqari)  Xususiy   hollarda :
a > 1   (a < - 1) 
sin x ≥ a  sin x ≤ a 
yechimi yo'q
(Х €  R ) Х €  R
(yechimi yo'q ) Trigonometrik tengsizliklarni yechishning umumiy hollari
tg x ≥ a  tg x ≤ a 
arctg a +  ?????? n ≤ x <  /2 + ?????? ?????? n
-  /2	
??????  +  ?????? n < x ≤ arctg a  + 	?????? n Trigonometrik tengsizliklarni yechishning umumiy hollari
ctg x ≥ a  ctg x ≤ a 
n < x ≤ arcctg a  +  n
arcctg a +  ?????? n ≤ x <   +??????   ?????? n

Trigonometrik tengsizliklarni yechish

cos x ≥ a cos x ≤ a |a| ≤ 1Trigonometrik tengsizliklarni yechishning umumiy hollari - arccos a + 2 ?????? n ≤ x ≤ arccos a + 2 ?????? n arccos a + 2 ?????? n ≤ x ≤ 2 ?????? - arccos a + 2 ?????? n

Xususiy hollarda cos x ≥ 0 cos x ≤ 0 - /2 + ?????? 2 ?????? n ≤ x ≤ /2 ?????? + 2 ?????? n ?????? /2 + 2 ?????? n ≤ x ≤ 3 /2 ?????? + 2 ?????? n

Xususiy hollarda ( а = -1 uchun ) 1) cos x ≥ 1 2) cos x > 1 1) X = 2?????? n 2) yechimi yo'q 1) cos x ≤ 1 2 ) cos x < 1 1) X € R 2) X € R , кроме 2 ?????? n

Xususiy hollarda : a > 1 (a < - 1) cos x ≥ a cos x ≤ a Yechimi yo’q (Х € R ) Х € R (yechimi yo’q )