√3tan10°+4sin10°
=2*(√3/2)tan10°+4sin10°
=2*sin60sin10°/cos10 +4sin10cos10/cos10
=2*(-1/2)(cos70-cos50)/cos10 + 2sin20/cos10
=(cos50-cos70)/cos10 + 2cos70/cos10
=(cos50-cos70+ 2cos70)/cos10
=(cos50+ cos70)/cos10
=(2cos60cos10)/cos10
=2cos60
=1