Prove (1-tan^2A)/(1+tan^2A)=cos2A , 是tanA的二次方, 不是tan2A啊
我把L.H.S.乘(1+tan^2A)/(1+tan^2A)
我解到NUMERATOR為1-tan^4A就計不下去了...
數學 Trigonometry 的Prove
2009-09-20 5:47 pm
回答 (1)
2009-09-20 5:59 pm
✔ 最佳答案
1 - tan^2 A = 1 - sin^2 A/cos^2 A = (cos^2 A - sin^2 A)/cos^2 A= cos2A/cos ^2 A.
1 + tan^2 A = 1 + sin^2 A/cos^2 A = (cos^2 A + sin^2 A)/cos^2 A
= 1/cos^2 A.
So dividing each other we get L.H.S. = cos2A = R.H.S.
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