cos20°-cos40°-cos80°的值为?

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cos20°-cos40°-cos80°的值为?cos20°-cos40°-cos80°的值为?cos20°-cos40°-cos80°的值为?cos40=cos(60-20)=cos60*cos20

cos20°-cos40°-cos80°的值为?
cos20°-cos40°-cos80°的值为?

cos20°-cos40°-cos80°的值为?
cos 40 = cos(60-20) = cos60*cos20+sin60*sin20
cos 80 = cos(60+20) = cos60*cos20-sin60*sin20
所以
代入原式得
cos20-(cos60*cos20+sin60*sin20)-(cos60*cos20-sin60*sin20)
=cos20-2cos60*cos20-sin60*sin20+sin60*sin20
=cos20-2cos60*cos20
=cos20-2*(1/2)*cos20
=0;

cos20-cos40-cos80
=cos(30-10)-cos(30+10)-cos80
=(cos30cos10+sin30sin10)-(cos30cos10-sin30sin10)-sin10 (和角公式,cos80=sin10 )
=2sin30sin10-sin10 (合并)
=sin10-sin10 (2sin30=1)
=0 。