cos@ cos2@ cos2^2@ cos2^3@ ... cos2^n @= sin2^(n+1) @/ 2^(n+1) sin @
( prove by MI , nis a positive integer)
A maths(MI)
2007-04-09 6:35 am
回答 (1)
2007-04-09 6:47 am
✔ 最佳答案
sin2^2@/2^2sin@=2sin2@cos2@/4sin@=4sin@cos@cos2@/4sin@=cos@cos2@so n=1 is right
suppose [email protected]^k@=sin2^(k+1)@/2^(k+1)sin@
[email protected]^k@cos2^(k+1)@=sin2^(k+1)@cos2^(k+1)@/2^(k+1)sin@
=2sin2^(k+1)@cos2^(k+1)@/2^(k+2)sin@=sin2^(k+2)@/2^(k+2)sin@
so n=k+1 is right
收錄日期: 2021-04-12 20:32:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070408000051KK05020