化简:(sin40°+sin80°)/cos20°

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化简:(sin40°+sin80°)/cos20°
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化简:(sin40°+sin80°)/cos20°
化简:(sin40°+sin80°)/cos20°

化简:(sin40°+sin80°)/cos20°
(sin40°+sin80°)/cos20°=2sin[(40°+80°)/2]*cos[(40°-80°)/2]/cos20°=√3
和差化积
sinθ+sinφ = 2 sin[(θ+φ)/2] cos[(θ-φ)/2]
sin40+sin80=2sin[(40+80)/2]*cos[(40-80)/2]=2sin60cos(-20)=2sin60cos20
其中cos(-θ)=cosθ

(sin40°+sin80°)/cos20°=2sin[(40°+80°)/2]*cos[(40°-80°)/2]/cos20°=√3