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18-Mavzu: Keltirish formulalari.

Trigonometrik funksiyalar yig'indisini va ayirmasini ko'paytmaga ke1tirish formulalari

Endi ikki argument kosinuslarining ko'paytmasini yig'indiga keltirish formulalarini ko’rib chiqamiz:

Agar bo'lsa, u holda quyidagi formulalar hosil bo’ladi:


Yarim burchak formulalari:


darajalarni tushirish formulalari:
.
1. Ayniyatlarni isbot qiling:
1) sin²x - sin²cos²x - cos⁴x = 1 - 2cos²x; 2) cos²x + sin²x cos⁴x - sin⁶x - 1 - 2sin⁴x;
3) 6(sin⁴x + cos⁴x) - 4(cos⁶x + sin⁶x) = 2.
2. Ifodalarni soddalashtiring:

1. 
   2cos(π + x) + 3cos(-x) + cos{π - x); 2) sin(π + x) - 2sin(π - x) - 3sin(-x);
   

1. 
   4cos(-x) + 5sin(π + x) - 2sin(π - x) - 6cos(π + x).
   

3. Quyidagi funksiyalarni juft-toqlikka tekshiring:
1) sin⁹x; 2) cos⁹x; 3) sin⁸x;
4) 5cos⁵x + 6cos⁴x; 5) 3sin³x-2sin²x; 6) 3sin³x + 4cos⁵x.
4. Sinus va kosinus funksiyalar qaysi choraklarda bir xil ishoraga ega?
5. Ayirmalarning ishoralarini aniqlang:
1) sin38° - sin40°; 2) cos51° - sos21°; 3)sin48° - sin52°;
4) sinl32^D-sinl52°; 5) sinl2° -cos732°.

1. 
   cosa = -0,5, 90° < a < 180° bo'lsa, sina, tga va ctga ni toping.
   
2. 
   Ifodalarni soddalashtiring:
   

1) ctg²a - cos²a + cos²actg²a; 2) cos²a + sin²atg²a - tg²a;
7. Barcha trigonometrik funksiyalarni
1) sina; 2) cosa; 3) tga; 4) ctga orqali ifodalang.
8.Agar cosx = -0,8; siny = 0,4; bo'lsa,quyidagilarni toping:
1) cos(x +y); 2) cos(x-y); 3) sin(x + >0; 4) sin(x-y).