Matematika

Pertanyaan

jika tanA = 3tanB, maka tan(A-B) = .... A. cos2B/2-cos2B B. cos2B/2+cos2B C. sin2B/2-cos2B D. sin2B/2+cos2B E. sin2B/2-cos3B

1 Jawaban

  • Jawab :

    tan a = 3 tan b

    tan (a - b)
    = (tan a - tan b) / (1 + tan a tan b)
    = (3 tan b - tan b) / (1 + 3 tan b tan b)
    = (2 sin b/cos b) / ((cos² b + 3 sin² b)/cos² b)
    = 2 sin b cos b / (cos² b + 3 sin² b)
    = sin 2b / (cos² b + 3(1 - cos² b))
    = sin 2b / (3 - 2 cos² b)

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