cos^2 (A)+sin^2 (A) = cos(A+B)
a. prove 2cos^2 (A) - 1 = 1- 2sin^2(A)
b. prove A/2 = Root( (cosA+1)/2)
b唔識做
trigonometic identity
2011-03-22 7:17 am
回答 (2)
2011-03-22 5:21 pm
✔ 最佳答案
b) Rewriting cos A as:cos A = cos [2(A/2)]
= 2 cos2 (A/2) - 1
Hence:
2 cos2 (A/2) = 1 + cos A
cos2 (A/2) = (1 + cos A)/2
cos (A/2) = √[(1 + cos A)/2] or - √[(1 + cos A)/2]
Note: We should be aware of which quadrant is the angle A/2 in so that we can accordingly assign a positive or negative value to cos (A/2)
參考: 原創答案
2011-03-22 7:26 am
b)
I think cos(A/2) = ±√(cosA+1) /2
You can start from double angle formula of cos function :
2cos²(A/2) - 1 = cos 2(A/2)
I think cos(A/2) = ±√(cosA+1) /2
You can start from double angle formula of cos function :
2cos²(A/2) - 1 = cos 2(A/2)
收錄日期: 2021-04-21 22:20:14
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https://hk.answers.yahoo.com/question/index?qid=20110321000051KK01441