Trigonometric Identities

micatkie

2013-05-12 9:40 am

✔ 最佳答案

L.H.S.
= cosec2θ - cot2θ
= (1 / sin2θ) - (cos2θ / sin2θ)
= [(sin²θ + cos²θ) / 2sinθcosθ] - [(cos²θ - sin²θ) / 2sinθcosθ]
= (sin²θ + cos²θ - cos²θ + sin²θ) / 2sinθcosθ
= 2sin²θ / 2sinθcosθ
= sinθ / cosθ
= tanθ
= R.H.S.

Hence, cosec2θ - cot2θ ≡ tanθ

2013-05-12 01:42:50 補充：
trigonometric identities used :
sin²θ + cos²θ = 1
cos2θ = cos²θ - sin²θ
sin2θ = 2sinθcosθ

參考: micatkie, micatkie

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用戶38102

2013-05-12 10:40 pm

L.H.S.= cosec2θ - cot2θ
= (1 / sin2θ) - (cos2θ / sin2θ)
= [(sin²θ + cos²θ) / 2sinθcosθ] - [(cos²θ - sin²θ) / 2sinθcosθ]
= (sin²θ + cos²θ - cos²θ + sin²θ) / 2sinθcosθ
= 2sin²θ / 2sinθcosθ
= sinθ / cosθ
= tanθ
= R.H.S.

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