sin50º(1+√3tan10º)的值为?

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sin50º(1+√3tan10º)的值为?
sin50º(1+√3tan10º)的值为?

sin50º(1+√3tan10º)的值为?
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