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(tan10°-√3)sin40°
=(tan10°-tan60°)sin40°
=(sin10°/cos10°-sin60°/cos60°)sin40°
=sin40°*(sin10°*cos60-cos10°*sin60°)/(cos10°*cos60°)
=sin40°*sin(10°-60°)/(cos10°*1/2)
=-2sin40°*sin50°/cos10°
=[cos(40°+50°)-cos(40°-50°)]/cos10°
=(cos90°-cos10°)/cos10°
=(0-cos10°)/cos10°
=-1
=(tan10°-tan60°)sin40°
=(sin10°/cos10°-sin60°/cos60°)sin40°
=sin40°*(sin10°*cos60-cos10°*sin60°)/(cos10°*cos60°)
=sin40°*sin(10°-60°)/(cos10°*1/2)
=-2sin40°*sin50°/cos10°
=[cos(40°+50°)-cos(40°-50°)]/cos10°
=(cos90°-cos10°)/cos10°
=(0-cos10°)/cos10°
=-1
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