Matematika

Pertanyaan

Bantu 12,13 dengan cara
Bantu 12,13 dengan cara

1 Jawaban

  • 12) (tan^2 x)/(1 + sec x) = 1
    tan^2 x = 1 + sec x
    (sin^2 x)/(cos^2 x) = 1 + 1/(cos x) ====> kedua ruas dikali cos^2 x
    sin^2 x = cos^2 x + cos x
    (1 - cos^2 x) = cos^2 x + cos x
    0 = 2 cos^2 x + cos x - 1
    Misal cos x = p
    2p^2 + p - 1 = 0
    (2p - 1)(p + 1) = 0
    p = 1/2 atau p = -1
    cos x = 1/2 => cos x = cos 60° = cos 300°
    cos x = -1 => cos x = cos 180°
    Karena 0 < x < 90 maka x = 60°

    13) cos 5π/6 = cos 5(180°)/6 = cos 150° = - cos 30° = -1/2 √3