Yeun Chit 發問時間: 科學數學 · 8 年前

關於trigonometric ratios f2 急

幫手計 計到有20點(要step)

1. sinθ/tan ²θ+sinθ

2.tanθ/cosθ-1/cos ² θ

3.1/sin ²θ-1/tan² θ-cos²θ

1 個解答

評分
  • 8 年前
    最佳解答

    1.

    [sinθ/tan²θ] + sinθ

    = [sinθ/(sin²θ/cos²θ)] + sinθ

    = (cos²θ/sinθ) + sinθ

    = (cos²θ/sinθ) + (sin²θ/sinθ)

    = (cos²θ + sin²θ)/sinθ

    = 1/sinθ

    =====

    2.

    sin²θ + cos²θ = 1

    Hence, cos²θ = 1 - sin²θ

    [tanθ/cosθ] - [1/cos²θ]

    = [(sinθ/cosθ)/cosθ] - [1/cos²θ]

    = (sinθ/cos²θ) - (1/cos²θ)

    = (sinθ - 1) / cos²θ

    = (sinθ - 1) / (1 - sin²θ)

    = -(1 - sinθ) / (1 + sinθ)(1 - sinθ)

    = -1/(1 + sinθ)

    =====

    3.

    (1/sin²θ) - [1/tan²θ] - cos²θ= (1/sin²θ) - [1/(sin²θ/cos²θ] - cos²θ= (1/sin²θ) - (cos²θ/sin²θ) - cos²θ= [(1 - cos²θ)/sin²θ] - cos²θ= [(sin²θ + cos²θ - cos²θ)/sin²θ] - cos²θ= [sin²θ/sin²θ] - cos²θ= 1 - cos²θ

    = sin²θ + cos²θ - cos²θ

    = sin²θ

    參考資料: sioieng
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