Prove that:
Sin^4 x- Cos^4 x = Sin^2 x - Cos^2 x
trig 數學問題
2007-04-29 2:08 pm
回答 (2)
2007-04-29 3:13 pm
✔ 最佳答案
sin^4 x - cos^4 x= (sin² x)² - (cos² x)²
= (sin² x + cos² x)(sin² x - cos² x) [ ∵ a² - b² = (a + b)(a - b) ]
= sin² x - cos² x [ ∵ sin² x + cos² x = 1 ]
2007-05-01 2:55 am
sin^4 x - cos^4 x
= (sin^2 x)^2 - (cos^2 x)^2
=(sin^2 x+ cos^2 x)( sin^2 x - cos^2 x)
= sin^2 x - cos^2 x
By law,
sin^2 x + cos^2 = 1
a^2 - b^2 =(a+b)(a-b)
= (sin^2 x)^2 - (cos^2 x)^2
=(sin^2 x+ cos^2 x)( sin^2 x - cos^2 x)
= sin^2 x - cos^2 x
By law,
sin^2 x + cos^2 = 1
a^2 - b^2 =(a+b)(a-b)
參考: Keith ^^
收錄日期: 2021-04-13 00:24:08
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070429000051KK00687