(sin50°(1+√3tan10°)-cos20

(sin50°(1+√3tan10°)-cos20°)/cos80°√(1-cos20°

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sin50°(1+√3 tan10°)-cos20°/cos80°√（1-cos20°）
=[sin50°(cos10°+√3 sin10°)/cos10°-cos20°]/√2sin²10°
=(1-cos20°)/√2sin²10°
=√2