證明下列各恒等式:
1. cosA - cos2A = 6sin² (A ∕ 2) - 8sin^4 (A ∕ 2)
F.4 附加數學 - 和差化積與積化和差公式
2008-01-30 4:31 am
回答 (2)
2008-01-30 4:50 am
✔ 最佳答案
1) L.H.S.= cosA﹣cos2A
= 1﹣2sin2(A/2)﹣(2cos2A﹣1)
= 1﹣2sin2(A/2)﹣2cos2A + 1
= 2﹣2sin2(A/2)﹣2[1﹣2sin2(A/2)]2
= 2﹣2sin2(A/2)﹣2 + 8 sin2(A/2)﹣8sin4(A/2)
= 6sin2(A/2)﹣8sin4(A/2)
= R.H.S.
根據公式：
cos2A = 1﹣2sin2A
cos2A = 2cos2A﹣1
2008-01-31 5:20 am
Excellent ~
收錄日期: 2021-04-23 22:36:46
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080129000051KK02781