求sin40°（tan10°—根3）的值

√3=tan60
原式=sin40(sin10/cos10-sin60/cos60)
=sin40(sin10cos60-cos10sin60)/cos10cos60
=sin40sin(10-60)/cos10cos60
=-sin40sin50/(1/2*cos10)
=-sin40cos40/(1/2*cos10)
=-1/2*sin80/(1/2*cos10)
=-1/2*cos10/(1/2*cos10)
=-1

(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