tolong yaa Jika sin a - sin b = 3/5 dan cos a + cos b = 4/5, maka nilai sin (a+b)?
Matematika
pelajar907
Pertanyaan
tolong yaa Jika sin a - sin b = 3/5 dan cos a + cos b = 4/5, maka nilai sin (a+b)?
1 Jawaban
-
1. Jawaban Anonyme
TriGonoMetRi
sin a - sin b = 3/5
cos a + cos b = 4/5
(sin a - sin b)² + (cos a + cos b)² = (3/5)² + (4/5)²
(sin² a + cos² a) + (sin² b + cos² b) - 2 sin a sin b + 2 cos a cos b = (9 + 16)/25
1 + 1 + 2(cos a cos b - sin a sin b) = 1
2 cos (a + b) = 1 - 2
cos (a + b) = -1/2
••
sin (a + b) = √(1 - cos² (a + b))
sin (a + b) = √(1 - 1/4)
sin (a + b) = 1/2 √3 ✔