Matematika

Pertanyaan

tolong yaa Jika sin a - sin b = 3/5 dan cos a + cos b = 4/5, maka nilai sin (a+b)?

1 Jawaban

  • 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 ✔

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