Question

化简sin50(1+√3tan10)

Answer 1

sin50(1+√3tan10)=2*sin50/cos10(1/2cos10+√3/2sin10)
=2*sin50*cos50/cos10
=sin100/cos10
=sin10/cos10=tan10

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