阿浪山
幼苗
共回答了23个问题采纳率:87% 举报
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(π/8)-sin(π/8)][cos²(π/8) +cos(π/8)·sin(π/8)+sin²(π/8)]}· {[cos(π/8)+sin(π/8)][cos²(π/8) -cos(π/8)·sin(π/8)+sin²(π/8)]}
=[cos²(π/8)-sin²(π/8)]·[1+cos(π/8)·sin(π/8)]·[1-cos(π/8)·sin(π/8)]
=cos(π/4)·[1+(1/2)sin(π/4)]·[1-(1/2)sin(π/4)
=(√2/2)·[1+(√2/4)]·[1-(√2/4)]
=7√2/16
1年前
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