Matematika

Pertanyaan

tan a= 3/4 dan tan b=1/7. nilai cos (a+b)

1 Jawaban

  • diketahui 
    tan a = 3/4
    maka
    sin a = 3/5
    cos a = 4/5

    tan b = 1/7
    --------------------------------
    7² + 1² = 50 = (5√2)²
    ----------------------------------
    maka
    sin b = (1/10)√2
    cos b = (7/10)√2

    jadi 
    cos(a + b)
    = (cos a . cos b) - (sin a . sin b)
    = ([4/5] [(7/10)√2]) - ([3/5] [(1/10)√2])
    = (28/50)√2 - (3/50)√2
    = (25/50)√2
    = (1/5)√2

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