Question

sin50º（1＋√3tan10º）怎么做

Answer 1

sin50º（1+√3tan10º）
=sin50*(√3*sin10+cos10)/cos10
=sin50*2*(√3/2*sin10+1/2*cos10)/cos10
=sin50/cos10*2*(cos30sin10+cos10sin30)
=sin50/cos10*2*sin40
=2*sin50*cos50/cos10
=sin100/cos10
=cos10/cos10
=1

Answer 2

sin50(1+√3tan10)
=sin50(1+tan(60)tan10))
=sin50(1+sin(60)sin10)/[cos(60)cos(10])
=sin(50)[sin60sin10+cos60cos10]/[cos60cos10]
=sin(50)cos(60-10)/[cos(60)cos(10)]
=sin(50)cos(50)/[cos(60)cos(10)]
=sin(100)/[2cos(60)cos(10)]
=sin(100)/cos(10)
=cos(10)/cos(10)=1