推 IamCuteGirl :大大 感謝@___@ 07/23 21:34
※ 編輯: LuisSantos (111.250.168.29), 07/23/2014 21:55:53
※ 引述《IamCuteGirl (CuteGirl5566)》之銘言:
: 1 1
: 設 cosθ=tanθ,則 _________ + _________ =
: 1+sinθ 1-sinθ ______________
: 不好意思 上來麻煩大家了...
sinθ
cosθ = tanθ = ------- => (cosθ)^2 = sinθ
cosθ
1 - (sinθ)^2 = sinθ
(sinθ)^2 + sinθ - 1 = 0
-1 ±√5
sinθ = ----------
2
-1 + √5
∵ |sinθ|≦1 ∴ sinθ = ----------
2
1 1
----------- + -----------
1 + sinθ 1 - sinθ
1 - sinθ + 1 + sinθ
= ------------------------
(1 + sinθ)(1 - sinθ)
2
= ---------------
1 - (sinθ)^2
2
= -----------
(cosθ)^2
2
= -------
sinθ
2
= --------------
(-1 + √5)/2
4
= ---------
√5 - 1
(4)(√5 + 1) (4)(√5 + 1)
= -------------------- = -------------- = √5 + 1
(√5 - 1)(√5 + 1) 5 - 1
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