Using the De Moivre’s theorem and the binomial expansion to prove:
i)cos4θ=cos^4(θ)-6cos^2(θ)sin^2(θ)+sin^4(θ)
ii)sin4θ=4(cos^3(θ)sin(θ)-cosθsin^3(θ))
mathematics
2014-03-02 2:57 am
回答 (1)
2014-03-02 4:51 am
✔ 最佳答案
(cosθ+isinθ)⁴ = cos4θ+isin4θ(cosθ+isinθ)⁴ = cos⁴θ + 4cos³θisinθ + 6cos²θi²sin²θ + 4cosθi³sin³θ + i⁴sin⁴θ
(cosθ+isinθ)⁴ = cos⁴θ - 6cos²θsin²θ + sin⁴θ + 4cos³θsinθi - 4cosθsin³θi
cos4θ = cos⁴θ - 6cos²θsin²θ + sin⁴θ
sin4θ = 4cos³θsinθ - 4cosθsin³θ
收錄日期: 2021-04-27 20:36:15
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140301000051KK00155