cos^275度+cos^215度+cos75度cos15度

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cos^275度+cos^215度+cos75度cos15度

原式=cos²75+sin²(90-15)+cos75sin(90-15)
=cos²75+sin²75+cos75sin75
=1+1/2*2cos75sin75
=1+1/2*sin150
=1+1/2*1/2
=5/4

解:由题意可得:
cos^2(75)+cos^2(15)+cos(75)cos(15)
=(sin15)^2+(cos15)^2+sin15cos15
=(sin15)^2+(cos15)^2+(sin30)/2
=1+1/4=5/4