三角计算题求（tan10°— 根号3）×sin40°的值.

(tan10°-根号3)×sin40°
=(sin10度/cos10度-sin60度/cos60度)*sin40度
=(sin10度cos60度-sin60度cos10度)*sin40度/(cos10度cos60度)
=-cos40度*sin40度/(cos10度cos60度)
=-sin80度/(2cos10度cos60度)
=-1/(2cos60度)
=-1

原式=(tan10-tan60)sin40
=(sin10/cos10-sin60/cos60)*sin40
=(sin10cos60-sin60cos10)*sin40/(cos10cos60)
=sin(10-60)*sin40/(cos10cos60)
=-sin50*sin40/(cos10cos60)
=-cos40*sin40/(cos10cos60)
=-sin80/(2cos10cos60)
=-cos10/(2cos10cos60)
=-1/(2cos60)
=-1