3-to’plam 29 may 2022

www.pedagoglar.uz
29-son 3 –to’plam may 2022 
Sahifa: 149 
O’quvchilar ayniy shakl almashtirishlarni yaxshi o’zlashtirishlari uchun 
birinchidan trigonometrik funksiyalar ta’rifini, ulardan birini ikkinchisi orqali 
ifodalovchi va asosiy ayniyatlar kabi formulalarni bilishlariga, ikkinchidan esa ana 
shu formulalarni trigonometrik ifoda berilishiga qarab tadbiq qila olish 
malakalariga bog’liqdir. Maktab matematika kursidagi trigonometrik ayniy shakl 
almashtirishlarni og’zaki bajarishga o’quvchilarni o’rgatish ularda mantiqiy 
matematik tafakkurni shakllantiradi. O’qituvchi biror trigonometrik ifodaning 
shaklini almashtirishni bajarishdan oldin o’quvchilarga eng sodda bo’lgan og’zaki 
trigonometrik mashqlardan namunalarni doskaga yozib, o’quvchilardan tezroq 
og’zaki soddalashtirishni bajarishlarini talab qilishi o’quvchilarni trigonometrik 
ayniyat va formulalarni esda doimo saqlashlariga imkon yaratadi.
Masalan, 
Bundan keyin o’qituvchi murakkabrok trigonometrik almashtirishlarni 
ko’rsatishi maqsadga muvofiqdir. 
1-misol. (1–sin

)(1+sin

)–cos
2

ifodani soddalashtiring. 
1-usul. 
2-usul. 
2 - misol. 
ifodani soddalashtiring.
Yuqoridagilardan ko’rinadiki, trigonometriya kursida ayniy almashtirishlar 
muhim o’rin egallaydi. O’quvchilar trigonometrik ayniy shakl almashtirishlarni 
yaxshi o’zlashtirishlari uchun birinchidan, trigonometrik funksiyalarni birini 
;
cos
;
1
;
1
;
;
cos
sin
);
cos
1
)(
cos
1
(
;
sin
1
;
cos
1
2
2















tg
ctg
tg
tg
ctg
ctg
tg
tg













.
0
cos
cos
1
1
cos
cos
1
1
cos
sin
1
cos
sin
1
sin
1
2
2
2
2
2
2
2
















a
a
a
a
a







;
0
1
1
)
cos
(sin
1
cos
sin
1
cos
sin
1
sin
1
2
2
2
2
2



















a




2
2
sec
sec
1
cos
cos
1






.
cos
1
cos
cos
cos
cos
1
cos
1
cos
cos
1
cos
1
1
1
cos
1
sec
sec
1
cos
1
2
2
2
2
2
2
2
2
2
2
2







































сos
сos
сos
сos
сos
сos

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www.pedagoglar.uz
29-son 3 –to’plam may 2022 
Sahifa: 150 
ikkinchisi orqali ifodalovchi va asosiy ayniyat kabi formulalarni, ikkinchidan esa 
shu formulalarni trigonometrik ifodani berilishiga qarab tadbiq qila olish 
malakalariga bog’liqdir. Trigonometrik ayniy shakl almashtirishlarni bajarish 
uchun quyidagi formulalarni bilishlari kerak:
1. Asosiy trigonometrik ayniyatlar:
Bu ayniyatlardan kelib chiqadigan formulalar quyidagilardir:
1-misol. Ayniyatni isbotlang. 
Isboti: 
 
Adabiyotlar 
1. Sh.Alinov,O.R.Xolmuhammedov,M.A.Mirzaxmedov. 9-―algebra‖ 2006- yil 
2. www.bilimdon.uz 
3. www.ziyonet.uz 
4. www.lex.uz 
5. www.matematika.ru 
;
,
)
1
2
(
2
,
cos
1
sec
)
4
);
(
,
sin
cos
)
3
;
,
)
1
2
(
2
,
cos
sin
)
2
;
1
cos
sin
)
1
2
2
Z
n
n
n
ctg
Z
n
n
tg




































.
),
(
,
sin
1
cos
)
5
Z
n
n
ec







.
,
2
1
)
1
Z
n
n
ctg
tg






 








.
,
,
cos
1
)
3
.
,
)
1
2
(
2
,
sec
1
)
2
2
2
2
2
Z
n
ec
ctg
Z
n
n
tg





















.
)
1
2
(
2
,
2
cos
sin
5
)
1
2
)(
2
(
cos
2










n
tg
tg







.
2
)
cos
(sin
2
cos
sin
5
cos
sin
cos
2
cos
sin
4
sin
2
cos
sin
5
1
cos
sin
2
2
cos
sin
cos
cos
sin
5
)
1
2
)(
2
(
cos
2
2
2
2
2
2


















































tg
tg

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www.pedagoglar.uz
29-son 3 –to’plam may 2022 
Sahifa: 151 
EFFECTS OF ORGANIZING CLASSES USING INTERACTIVE 
METHODS IN ENGLISH LESSONS IN SECONDARY SCHOOLS. 
Maloxatxon Atamuratova Muratboyevna 
The Republic of Karakalpakstan Amudarya district belongs to XTB High 
School N-2 English teacher 
 
Annotation:Today, the younger generation is increasingly interested in
learning foreign languages. therefore, teaching a foreign language, including 
English, in secondary schools requires the use of interactive methods in the 
classroom. This article focuses on the effectiveness of organizing lessons using 
interactive methods in English classes in secondary schools. 
 
Keywords: Method, interactive method, information and communication 
technologies, interactivity. 
Significant work is being done in our country to form an information society, to 
introduce the most advanced information and communication technologies in all 
areas. In particular, the capabilities of interactive services in this process are highly 
valued. The Uzbek dictionary defines the term “interactive” as based on the 
reception or transmission of information over a computer network. In Wikipedia, 
interactivity is rated as a concept that reveals the nature and level of interaction 
between objects and is said to be used in information theory, computer science and 
programming, telecommunications systems, sociology, industrial design, and 
more. in other words, interactivity is a system of organizing the system to achieve 
a specific goal by establishing the exchange of information between parts of the 
system. 
The interactive method is aimed at activating the acquisition of knowledge and 
developing personal qualities of students by increasing the activity between 
students and the teacher in the educational process. Using interactive methods can 
help increase lesson effectiveness. The main criteria of interactive education: 

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