cos^6(π/8)-sin^6(π/8)=求值,[cos^2(π/8)-sin^2(π/8)][cos^4(π/8)+sin^4_数学解答

cos^6(π/8)-sin^6(π/8)=求值,
[cos^2(π/8)-sin^2(π/8)][cos^4(π/8)+sin^4(π/8)+cos^2(π/8)sin^2(π/8)]
=cos(π/4)[1-cos^2(π/8)sin^2(π/8)]
=cos(π/4)[1-[sin^2(π/4)]/4]
==7√2/16

人气：307 ℃　时间：2020-05-11 01:52:54

解答

知识储备：a³ +b³ = (a+b)(a²-ab +b²) a³ -b³= (a-b)(a² +ab +b²) cos^6(π/8)-sin^6(π/8)=[cos³(π/8)-sin³(π/8)]·[cos³(π/8)+sin³(π/8)]={[cos...