Question

化简 sin40°(tan10°-√3)

Answer 1

sin40°乘于（tan10°－根号3）
=sin40°*(sin10°/cos10°-sin60°/cos60°)
=sin40°[(sin10°cos60°-cos10°sin60°)/cos10°cos60°]
=sin40°*(-sin50°)/(1/2*cos10°)
=-2sin40°sin50°/cos10°
=-2sin40°cos40°/cos10°
=-sin80°/cos10°
=-1

Answer 2

答：
sin40°(tan10°-√3)
=sin40°(sin10°-√3cos10°) /cos10°
=2sin40°*[(1/2)sin10°-(√3/2)cos10°] / cos10°
=2sin40°sin(10°-60°) /cos10°
=-2sin40°sin50° /cos10°
=-2sin40°cos40° /cos10°
=-sin80° /sin80°
=-1