Prove
cos^4a = 3/8 + 1/2 cos(2a) + 1/8 cos a
trigonometric again help help!!!
2007-11-25 7:56 am
回答 (1)
2007-11-25 10:17 am
✔ 最佳答案
I think you want to provecos^4a = 3/8 + 1/2 cos(2a) + 1/8 cos(4a)
Since
cos(2a)=2cos^2a-1
cos(4a)=2cos^2(2a)-1=2[(2cos^2a-1)^2]-1=2(4cos^4a-4cos^2a+1)-1
=8cos^4a-8cos^2a+1
RHS
=3/8 + 1/2 cos(2a) + 1/8 cos(4a)
=3/8 + 1/2 (2cos^2a-1) + 1/8 (8cos^4a-8cos^2a+1)
=3/8 + cos^2a-1/2 + cos^4a-cos^2a+1/8
=cos^4a
=LHS
收錄日期: 2021-04-25 16:54:11
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https://hk.answers.yahoo.com/question/index?qid=20071124000051KK05354