13(a)以cos x 表示 1-tan^2x / 1+tan^2x
(b)由此,解方程 1-tan^2x / 1+tan^2x = cos x, 其中0≦x≦360.
F.5 三角學
2012-08-21 2:18 am
回答 (1)
2012-08-21 3:04 am
✔ 最佳答案
(a)1-tan^2x / 1+tan^2x
=(1-sin^2x/cos^2x) / (1+sin^2x/cos^2x)
=[(cos^2x-sin^2x)/cos^2x] / (1/cos^2x)
=cos^2x-sin^2x
=cos^2x-(1-cos^2x)
=2cos^2x-1
(b)
1-tan^2x / 1+tan^2x = cosx
2cos^2x-1 = cosx
2cos^2x-cosx-1 = 0
(cosx-1)(2cosx+1)=0
cosx=1 or cosx=-1/2(rejected)
∴cosx=1
∴x=0 or 360
參考: me
收錄日期: 2021-04-20 13:10:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120820000051KK00705