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问题: 一道高一的数学题,谢谢高手们,不难,大家看看啊

求2cos10°-sin20°/cos20°的值

解答:

(2cos10-sin20)/cos20
=(2sin80-sin20)/cos20
=[sin80+(sin80-sin20)]/cos20
={sin80+[sin(50+30)-sin(50-30)]}/con20
={sin80+[sin50cos30+cos50sin30-(sin50cos30-cos50sin30)]}/cos20
=(cos10+2cos50sin30)/cos20
=[cos(30-20)+2*1/2*cos(30+20)]/cos20
=[(cos30cos20+sin30sin20)+(cos30cos20-sin30sin20)]/cos20
=(2cos30cos20)/cos20
=2cos30
2*3^.5/2
=3^(1/2)