因为sin50°(1+√3sin10°/cos10°)=sin50°(cos10°+√3sin10°)/cos10°
=2sin50°(cos60°cos10°+sin60°sin10°)/cos10°
=2sin50°cos50°/sin10°=sin100°/cos10°=sin80°/cos10°=cos10°/cos10°=1,
所以分子=1-cos20°,
原式=√(1-cos20°)/sin10°=√[1-(1-2sin²10°]/sin10°=√2sin10°/sin10°=√2
因为sin50°(1+√3sin10°/cos10°)=sin50°(cos10°+√3sin10°)/cos10°
=2sin50°(cos60°cos10°+sin60°sin10°)/cos10°
=2sin50°cos50°/sin10°=sin100°/cos10°=sin80°/cos10°=cos10°/cos10°=1,
所以分子=1-cos20°,
原式=√(1-cos20°)/sin10°=√[1-(1-2sin²10°]/sin10°=√2sin10°/sin10°=√2