化简sin50度（1+根号3倍tan10度）

网友回答

原式=sin50(1+tan60tan10)
=sin50(tan60-tan10)/tan(60-10)
=cos50(tan60-tan10)
=cos50(sin60cos10-sin10cos50)/cos60cos10
=cos50sin50/cos60cos10
=cos10/(2*1/2*cos10)
=cos10/cos10
=1======以下答案可供参考======
供参考答案1:
原式=sin50°[cos10°＋√3sin10°]/(cos10°)
=[(cos40°)/(cos10°)]×[2sin40°]
=sin80°/cos10°
=1供参考答案2:
顶楼上供参考答案3:
【1】1+(√3)tan10
=1+(√3)[sin10/cos10] (∵tan10=sin10/cos10 )
=[2/cos10]×[(1/2)cos10+(√3/2)sin10]
=[2/cos10]×[sin30cos10+cos30sin10]
=[2/cos10]sin40. (∵sin40=sin(30+10)=sin30cos10+cos10sin30]
=(2cos50)/cos10. (∵sin40=sin[90-50]=cos50. )
【2】原式=（2sin50cos50)/cos10
=(sin100)/cos10
=cos10/cos10
=1