How to prove the identity cos^4x-sin^4x+1=2cos^2x?
回答 (1)
2013-03-13 6:54 am
cos^4x - sin^4x + 1
= (cos^2x)^2 - (sin^2x)^2 + 1
= (cos^2x + sin^2x)(cos^2x - sin^2x) + 1
= cos^2x - sin^2x + 1
= cos^2x - sin^2x + sin^2x + cos^2x
= 2cos^2x
= (cos^2x)^2 - (sin^2x)^2 + 1
= (cos^2x + sin^2x)(cos^2x - sin^2x) + 1
= cos^2x - sin^2x + 1
= cos^2x - sin^2x + sin^2x + cos^2x
= 2cos^2x
收錄日期: 2021-05-01 13:47:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130312220158AAFxYfX