1) Express cot 3θ in terms of cot θ.
2.) prove that cos^2 (x-y ) - sin^2 (x+y ) = cos2x cos 2y
要有詳細步驟 thx
a maths Δ
2009-02-09 7:59 am
回答 (1)
2009-02-09 8:58 am
✔ 最佳答案
tan3x=(3tanx-tan^3x)/(1-3tan^2x)cot3x
=(1-3tan^2x)/(3tanx-tan^3x)
=(1-3/cot^2x)/(3/cotx-1/cot^3x)
=(cot^3x-3cotx)/(3cot^2x-1)
2
cos^2 (x-y ) - sin^2 (x+y )
=[cos(x-y)+sin(x+y)[cos(x-y)-sin(x+y)]
=[cosxcosy+sinxsiny+sinxcosy+cosxsiny][cosxcosy+sinxsiny-sinxcosy-cosxsiny]
=[(sinx+cosx)(siny+cosy)][(sinx-cosx)(siny-cosy)]
=[(sinx+cosx)(sinx-cosx)][(siny+cosy)(siny-cosy)]
=cos2xcos2y
收錄日期: 2021-04-15 21:22:58
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