MQ46 --- Series

2012-09-16 5:10 am
MQ46 --- SeriesDifficulty: 35%Evaluate ∏(k = 0 to n)cos2ᵏx.

回答 (1)

2012-09-16 9:35 am
✔ 最佳答案
cosx cos2x cos4x ... cos(2^n x)
=sinx cosx cos2x cos4x ... cos(2^n x) / sinx
=(1/2) sin2x cos2x cos4x ... cos(2^n x) / sinx
=(1/2)^2 sin4x cos4x ... cos(2^n x) / sinx
=(1/2)^3 sin8x cos8x... cos(2^n x) / sinx
= ...
=(1/2)^(n+1) sin[2^(n+1) x] / sinx


收錄日期: 2021-04-13 18:59:37
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120915000051KK00673

檢視 Wayback Machine 備份