Jika cos (A+B) = 100/125 dan cos (A-B)= -44/125 , maka nilai dari tan A x tan B adalah
Matematika
AurelliaLT
Pertanyaan
Jika cos (A+B) = 100/125 dan cos (A-B)= -44/125 , maka nilai dari tan A x tan B adalah
1 Jawaban
-
1. Jawaban whongaliem
cos (A + B) = 100/125
cos A .cos B - sin A .sin B = 100 / 125 ........ pers I
cos (A - B) = - 44/125
cos A .cos B + sin A .sin B = - 44 / 125 ..... pers II
elemenasi pers I dan II
cos A .cos B - sin A .sin B = 100/125
cos A .cos B + sin A .sin B = - 44/125
------------------------------------------------------- -
- 2.sin A .sin B = 144/125
sin A .sin B = (144/125) / 2
sin A .sin B = 72/125
cos A .cos B - sin A .sin B = 100/125
cos A .cos B - (72/125) = 100/125
cos A .cos B = (100/125) + (72/125)
cos A .cos B = 172/125
tan A x tan B = (sin A / cos A) x (sin B /cos B)
= (sin A .sin B) / (cos A .cos B)
= (72/125) / (172/125)
= (72/125) x (125/172)
= 72/172
= 18/43