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Trigonometrik funksiyalarning birini ikkinchisi orqali
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Trigonometrik funksiyalarning birini ikkinchisi orqali ifodalash 1.
2 2 2 1 cos
1 sin 1 1 ctg ctg tg a a a a a = ± - = ± = ± + + . 2.
2 2 2 1 sin
1 co s
1 1
tg ctg a a a a a = ± - = ± = ± + + . 3.
2 2 1 1 cos
sin cos
1 sin
tg ctg a a a a a a - = = ± = ±
- . 4. 2 2 1 1 s in
c o s s in
1 c o s
c tg tg a a a a a a - = = ± = ±
- .
A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m 47 a - ning qaysi chorakka tegishliligiga qarab "+" yoki "-" ishoradan biri olinadi. Masalan: Agar 0; 2 p a æ ö Îç ÷ è ø , ya`ni I-chorakda bo`lsa, 1- formulada + olinadi; agar 3 ; 2 p a p æ ö Îç ÷ è ø , ya`ni III-chorakda bo`lsa, 1- formulada - olinadi. Qo'shish formulalari 1.
(
)
. cos cos cos sin sin a b a b a b + = - 2.
(
)
. cos cos cos sin sin a b a b a b - = + 3 .
(
)
.
sin co s co s sin a b a b a b + = + 4 .
(
)
.
sin co s co s sin a b a b a b - = - 5 .
( ) 1 tg tg tg tg tg a b a b a b ± ± = × m . 1 6. ( ) ctg ctg ctg ctg ctg a b a b a b × ± = ± m . Karrali burchaklar 1. 2 2
. sin sin cos a a a = 2 2 2. 2
cos cos sin a a a = - 2 2 3. 2 . 1 tg sin tg a a a = + 2 2 1 4.
2 . 1
cos tg a a a - = + 2 2 5.
2 2
1 1 2 . cos cos sin a a a = - = - 2 2 6. 2 . 1
tg tg a a a = - 2 1 7. 2 . 2 ctg ctg ctg a a a - = 2 8. 2
. tg ctg tg a a a = - 3 9. 3
3 - 4
. sin sin sin a a a = 3 10. 3 4 - 3 cos cos cos a a a = 3 2 3 11. 3 . 1 3
tg tg tg tg a a a a - = - 3 2 3 12. 3 . 1 3 ctg ctg ctg ctg a a a a - = - ( ) 3 13. 4 4
- 8 . sin cos sin sin a a a a = × 4 2 14. 4 8 8 1. cos cos cos a a a = - + ( ) 2 2 4 4 1 15. 4 . 1 6
tg tg tg tg tg a a a a a × - = - + ( ) 4 2 2 2 6 1 16. 4 . 4 1 ctg ctg ctg ctg ctg a a a a a - + = × -
1. 2
2 2
sin a a - = . 2. 2 1 2 2 cos cos a a + = . Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m 48 3. 3 3 3 4 sin cos sin a a a - = . 4. 3 3 cos 3 4
cos a a a + = . 5. 2 1 2 1 2 cos tg cos a a a - = + . 6. 2 1
1 2
ctg cos a a a + = - . 7. 4 4 sin 2 cos cos a a a - = - . 8. 4 4 2 cos sin cos a a a - = . 9. ( ) 4 1 4 4 2 3 . 8
cos cos a a a = - + 10.
( ) 4 1 4 4 2 3 .
8 cos cos cos a a a = + + 11.
4 4 3 1 4 .
4 4
sin cos a a a + = + 12. 6 6 5 3 4 . 8 8
sin cos a a a + = + Yarim burchak uchun formulalar 1) 2 2 1 2 2 cos sin a a + = ; 2) 2 2 2 sin sin co s a a a = ; 3) 2 2 2 2
cos sin a a a = - ; 4) 1 2 2 cos sin a a - = ±
; 5) 1 2 2
cos a a + = ±
; 6) 1 2 1 cos tg cos a a a - = ± + ; 7) 1 2 1 cos ctg cos a a a + = ± - ; 8) 2 1
2 cos cos a a + = ; 9) 2 1 2 2
sin a a - = ; 10) 2 1 2 1 cos tg cos a a a - = + ; 11) 2 1 2 1 cos ctg cos a a a + = - ; 12) 2 2
2 2
ctg a a × = ; 13) 1 2 1 cos sin ctg sin cos a a a a a + = = - ; 14)
1 2 1 cos sin tg sin cos a a a a a - = = + .
orqali ifodasi 1) 2 2 1 2 2 sin tg tg a a a æ ö = + ç ÷ è ø ; 2) 2 2 1 1 2 2 cos tg tg a a a æ ö æ ö = - + ç ÷ ç ÷ è ø è ø ; 3) 2 2 1 2 2
tg tg a a a æ ö = - ç ÷ è ø ; 4) 2 1 2 2 2 c tg tg tg a a a æ ö = - ç ÷ è ø . Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m 49 Ko'paytmani yig'indiga keltirish 1. ( ) ( ) 1 2
cos sin sin a b a b a b
× = + + - é ù ë û . 2. ( ) ( ) 1 2 cos cos cos cos a b a b a b
× = + + - é ù ë û . 3. ( ) ( ) 1 2
sin cos cos a b a b a b
× = - - + é ù ë û . 4. tg tg tg tg tg tg ctg ctg ctg ctg a b b a a b a b b a + - × = = + - . 5.
ctg ctg ctg ctg ctg tg tg tg tg a b b a a b a b a b + - × = = + - . 6.
ctg tg ctg tg ctg ctg tg tg ctg a b a b a b a b b a + - × = = + - . 7. 1 1 2 2 4 ...
2 2
n n sin co s co s co s co s sin a a a a a a + + × × × × = . 8. 2 3 1 ... 2 1 2 1 2 1 2 1 2 n n cos cos cos cos n n n n p p p p × × × ×
= + + + + . Masalan: 2 2 1 ) ,
5 2 2 1,
2 5 5 2 a cos cos n p p × = = × + = ; 7 2 7 1 ) ... , 15 2 7 1,
7 15 15 15 2
cos cos cos n p p p × × × = = × +
= . 9. 1 2 ... 2 4 2 2 2
n n sin co s co s co s co s sin a a a a a a + × × × ×
= .
1. 2
2 sin sin sin cos a b
a b a b + - + = × . 2. 2 2 2 sin sin sin cos a b
a b a b - + - = × . 3. 2 2 2 cos cos cos cos a b
a b a b + - + = × . 4. 2 2 2 cos cos sin sin a b
a b a b + - - =- × . 5. ( ) sin tg tg cos cos a b
a b a b + + = × . 6. ( )
tg tg cos cos a b
a b a b - - = × . Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o Download 0.8 Mb. Do'stlaringiz bilan baham: 
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