化简sin50°（1+根号3tan10°）

如题所述

第1个回答 2012-01-05

sin50度(1+根号3乘sin10除以cos10)
=sin50度(cos10度+根号3乘sin10）除以cos10
=sin50度(2sin40)除以cos10
=cos40度(2sin40)除以cos10
=sin80除以cos10=1

第2个回答 2012-01-05

(1+√3tan10)=(-cos120cos10+sin120sin10)*2/cos10=-2cos130/cos10=2cos50/cos10
sin50*(1+√3tan10)=(2sin50cos50)/cos10=sin100/cos10=sin80/cos10=cos10/cos10=1本回答被提问者采纳

第3个回答 2012-01-05

原式=sin50°[cos10°＋√3sin10°]/cos10°
=sin50°[2sin(30°＋10°)]/cos10°
=[2cos40°sin40°]/cos10°
=sin80°/cos10°
=cos10°/sin10°
=1

第4个回答 2012-01-05

sin50°(1+√3tan10°)
=sin50°[1+√3(sin10°/cos10°)]
=sin50[(cos10+√3sin10)/cos10]
=sin50°[2sin(30+10)/cos10°]
=(2sin50°sin40°)/cos10°
=(2cos40°*sin40°)/cos10°
=cos10°/cos10°
=1

第5个回答 2012-01-17

原式=sin50°[cos10°＋√3sin10°]/cos10°
=sin50°[2sin(30°＋10°)]/cos10°
=[2cos40°sin40°]/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1

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