Matematika

Pertanyaan

tolong dibantoo yaaaa flisss (tan 45 persen )²..... ketinggalan tadi pangkat 2
tolong dibantoo yaaaa flisss (tan 45 persen )²..... ketinggalan tadi pangkat 2

1 Jawaban

  • Mapel : Matematika
    Kelas : X SMA
    Bab : Trigonometri

    Pembahasan :
    Cos 45° / Sec 30° + Cosec 30°
    = (1/2 √2) / [(2/3 √3) + 2]
    = (3√2) / [(4√3 + 2)]
    = (3√2)(4√3 - 2) / (4√3 + 2)(4√3 - 2)
    = (12√6 - 6√2)/(48 - 4)
    = (12√6 - 6√2)/44
    = (6 - 3√2)/22

    ————————————————
    [Sin 30° + Tan 45° - Cosec 60°]/[Sec 30° + Cos 60° + Cot 45°]
    = [1/2 + 1 - 2/3√3]/[2/3 √3 + 1/2 + 1]
    = [3/2 - 2/3√3]/[2/3√3 + 3/2]
    = [9 - 4√3]/[4√3 + 9]
    = (9 - 4√3)(4√3 - 9)/(4√3 + 9)(4√3 - 9)
    = (72√3 - 129)/(48 - 81)
    = (72√3 - 129)/-33
    = (129 - 72√3)/33

    ————————————————
    [2(Cos 60°)² + 4(Sec 30°)² - (Tan 45°)²]/[(Sin 30°)² + (Cos 30°)²]
    = [2(1/2)² + 4(2/3 √3)² - (1)²]/[(1/2)² + (1/2√3)²]
    = [2(1/4) + 4(12/9) - 1]/[1/4 + 3/4]
    = [1/2 + 48/9 - 1]/1
    = (9 + 96 - 18)/18
    = 84/18
    = 42/9