Prove that
(tanθ sinθ) / (tanθ + sinθ) ≡ (tanθ - sinθ) / (tanθ sinθ)
maths.... trigo.... identity
2008-03-02 7:52 pm
回答 (1)
2008-03-02 8:08 pm
✔ 最佳答案
L.H.S.= (tanθ sinθ) / (tanθ + sinθ)
= sinθ (tanθ) / [sinθ (1/cosθ + 1)]
= tanθ / (1/cosθ + 1)
= (sinθ/cosθ) / (1/cosθ + 1)
= sinθ / (1 + cosθ)
= sinθ(1 - cosθ) / (1 - cos^2 θ)
= (1 - cosθ) / sin θ
= tanθ(1 - cosθ) / (tanθ sinθ)
= (tanθ - sinθ) / (tanθ sinθ)
= R.H.S.
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