sin6x+cos6x,
is it equal to (sin2x+cos2x)(sin4x-2sin2xcos2x+cos4x)
or just equal to (sin2x+cos2x)(sin4x-sin2xcos2x+cos4x)
which one is correct?
Maths , solve problem (aid)
2007-03-02 4:47 pm
回答 (1)
2007-03-02 5:13 pm
✔ 最佳答案
sin6x + cos6x=(sin2x)3 + (cos2x)3
= (sin2x + cos2x)(sin4x - sin2xcos2x + cos4x)...(*)
= (1)(sin4x - sin2xcos2x + cos4x)
= (sin2x + cos2x)2 - 3sin2xcos2x
= 1 - 3sin2xcos2x
按:
(*)用了a^3 + b^3 = (a+b)(a^2 - ab + b^2)
和 cosxcosx + sinxsinx = 1
兩個 properties
收錄日期: 2021-04-12 23:46:36
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