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ºÂɸ¤ËľÀþBD¤ÈAC¤Î¸òÅÀ¤òE(0,0),B(-2,0)¤È¤·¤Æ
ľÀþBC:y=-sqrt(3)*(x+2)/3,AC:y=sqrt(3)*x¤Î¸òÅÀC¤òµá¤á¤ë¤È
solve([y=-sqrt(3)*(x+2)/3,y=-sqrt(3)*x],[x,y]);x=1,y=-sqrt(3)
¤³¤³¤Çtan(20¡ë)=tan(a)¤È¤·¤Æ
¸òÅÀC¤òÄ̤극¤­-tan(2*a)=-2*tan(a)/(1-tan(a)^2)¤ÎľÀþCD:y=-2*tan(a)*(x-1)/(1-tan(a)^2)-sqrt(3)¤Èx¼´¤Î¸òÅÀD¤òµá¤á¤ë¤È
solve(0=-2*tan(a)*(x-1)/(1-tan(a)^2)-sqrt(3),x);x=(sqrt(3)*tan(a)^2+2*tan(a)-sqrt(3))/(2*tan(a))
ľÀþBA:y=tan(a)*x,AC:y=-sqrt(3)*x¤Î¸òÅÀA¤òµá¤á
solve([y=tan(a)*(x+2),y=-sqrt(3)*x],[x,y]);x=-2*tan(a)/(tan(a)+sqrt(3)),y=2*sqrt(3)*tan(a)/(tan(a)+sqrt(3))
DA^2¤ò»°Ê¿Êý¤Çµá¤á
factor((-2*tan(a)/(tan(a)+sqrt(3))-(sqrt(3)*tan(a)^2+2*tan(a)-sqrt(3))/(2*tan(a)))^2+(2*sqrt(3)*tan(a)/(tan(a)+sqrt(3)))^2);
3*(tan(a)^6+2*3^(3/2)*tan(a)^5+45*tan(a)^4+4*sqrt(3)*tan(a)^3-17*tan(a)^2-2*sqrt(3)*tan(a)+3)/(4*tan(a)^2*(tan(a)+sqrt(3))^2)
BD^2=(D¤ÎxºÂɸ+2)^2¤òµá¤á
factor(expand(((sqrt(3)*tan(a)^2+2*tan(a)-sqrt(3))/(2*tan(a))+2)^2));
3*(tan(a)^4+4*sqrt(3)*tan(a)^3+10*tan(a)^2-4*sqrt(3)*tan(a)+1)/(4*tan(a)^2)
DA^2=BD^2¤È¤·¤ÆƱ¤¸°ø¿ô¤ò¾Ãµî¤·¤Æ
(tan(a)^6+2*3^(3/2)*tan(a)^5+45*tan(a)^4+4*sqrt(3)*tan(a)^3-17*tan(a)^2-2*sqrt(3)*tan(a)+3)/(tan(a)+sqrt(3))^2=
(tan(a)^4+4*sqrt(3)*tan(a)^3+10*tan(a)^2-4*sqrt(3)*tan(a)+1)¡¡º¸ÊÕ¤ÎʬÊì¤ò±¦Êդ˳ݤ±¤Æº¸ÊÕ¤Îʬ»Ò¤ò°ú¤¤¤Æ°ø¿ôʬ²ò¤¹¤ë¤È
factor((tan(a)+sqrt(3))^2*(tan(a)^4+4*sqrt(3)*tan(a)^3+10*tan(a)^2-4*sqrt(3)*tan(a)+1)-(tan(a)^6+2*3^(3/2)*tan(a)^5+45*tan(a)^4+4*sqrt(3)*tan(a)^3-17*tan(a)^2-2*sqrt(3)*tan(a)+3));
-8*tan(a)*(tan(a)^3-3^(3/2)*tan(a)^2-3*tan(a)+sqrt(3)¡¦¡¦¡¦¡¦¡¦¡¦(1)
¤³¤³¤Ç¡¡tan(60¡ë)=(3*tan(a)-tan(a)^3)/(1-3*tan(a)^2)=sqrt(3)¡¡¤è¤ê
sqrt(3)-3*sqrt(3)*tan(a)^2=3*tan(a)-tan(a)^3¡¡tan(a)^3=3*sqrt(3)*tan(a)^2+3*tan(a)-sqrt(3)
¤³¤ì¤È(1)¤È¤è¤ê(1)=0 ¤è¤ê¡¡DA^2=BD^2¡¡DA=BD ¤è¤ê
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ľÀþBD¤ÈAC¤Î¸òÅÀ¤òE(sqrt(1+tan(20*%pi/180)),0),D(0,0),B(-2,0)¤È¤¹¤ë¤È¡¦¡¦¡¦
A((sqrt(1+tan(20*%pi/180))-2)/2,tan(20*%pi/180)*(2+sqrt(1+tan(20*%pi/180))/(1-tan(20*%pi/180)^2))
BD=2 BD^2=4 ¤Ç¡¡¤³¤³¤Çtan(20¡ë)=tan(a)¤È¤·¤Æ»°Ê¿Êý¤Ç¡¡BA^2¤òµá¤á¤ë¤È
factor(((sqrt(1+tan(a)^2)-2)/2+2)^2+tan(a)^2*(2+sqrt(1+tan(a)^2))^2/(1-tan(a)^2)^2);
(tan(a)^2+1)^2*(sqrt(tan(a)^2+1)+2)^2/(4*(tan(a)-1)^2*(tan(a)+1)^2)¤³¤ì¤¬4(=BD^2)¤È¤¹¤ë¤È
factor((tan(a)^2+1)^2*(sqrt(tan(a)^2+1)+2)^2-4*4*(tan(a)-1)^2*(tan(a)+1)^2);
4*tan(a)^4*sqrt(tan(a)^2+1)+8*tan(a)^2*sqrt(tan(a)^2+1)+4*sqrt(tan(a)^2+1)+tan(a)^6-9*tan(a)^4+43*tan(a)^2-11
tan(a)^2+1=1/cos(a)^2 sqrt(tan(a)^2+1)=1/cos(a) ¤ÇºÇ½é¤Î3¹à¤Ï
(4*tan(a)^4+8*tan(a)^2+4)/cos(a)=4*(tan(a)^2+1)^2/cos(a)=4/cos(a)^5 »Ä¤ê¤Î4¹à¤Ï
tan(a)^2=1/cos(a)^2-1 ¤è¤ê
factor((1/cos(a)^2-1)^3-9*(1/cos(a)^2-1)^2+43*(1/cos(a)^2-1)-11);
-(64*cos(a)^6-64*cos(a)^4+12*cos(a)^2-1)/cos(a)^6
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factor(4/cos(a)^5-(64*cos(a)^6-64*cos(a)^4+12*cos(a)^2-1)/cos(a)^6);
-(8*cos(a)^3-6*cos(a)-1)*(8*cos(a)^3-2*cos(a)+1)/cos(a)^6¡¦¡¦¡¦¡¦¡¦¡¦(1)
¤³¤³¤Çcos¤Î3ÇܳѤθø¼°¤è¤ê¡¡4*cos(a)^3-3*cos(a)=cos(60*%pi/180)=1/2¡¡¤è¤ê¡¡8*cos(a)^3-6*cos(a)=1
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(2m+2n+59)(55+2n-2m)=59*55
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