Prove that
tan^2 x - sin^2 x= (tan x sin x)^2
Trigo 問題
2009-03-07 7:53 pm
回答 (2)
2009-03-07 8:12 pm
✔ 最佳答案
Tan^2 x - Sin^2 x= (Tan x Sin x)^2sol:
(Tanx Sinx)^2+Sin^2x
=Tan^2x Sin^2x+Sin^2x
=(Tan^2x+1)*Sin^2x
=Sec^2x*Sin^2x
=(1/Cos^2x)*Sin^2
=Tan^2x
so Tan^2 x - Sin^2 x= (Tan x Sin x)^2
2009-03-08 9:10 am
Let θ be x,
tan2θ - sin2θ = (tanθsinθ) 2
L.H.S. = tan2θ - sin2θ
= sin2θ / cos2θ - sin2θ
= sin2θ - sin2θcos2θ / cos2θ
= sin2θ (1 - cos2θ) / cos2θ
= sin2θsin2θ / cos2θ
= sin2θtan2θ
= (tanθsinθ)2
= R.H.S.
∴tan2θ - sin2θ = (tanθsinθ) 2
tan2θ - sin2θ = (tanθsinθ) 2
L.H.S. = tan2θ - sin2θ
= sin2θ / cos2θ - sin2θ
= sin2θ - sin2θcos2θ / cos2θ
= sin2θ (1 - cos2θ) / cos2θ
= sin2θsin2θ / cos2θ
= sin2θtan2θ
= (tanθsinθ)2
= R.H.S.
∴tan2θ - sin2θ = (tanθsinθ) 2
參考: me
收錄日期: 2021-04-13 16:30:00
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