(sin20°-sin80°)/(cos20°-cos80°)怎么化= = 脑子不大灵光

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(sin20°-sin80°)/(cos20°-cos80°)怎么化
= = 脑子不大灵光

分子
=sin(50-30)-sin(50+30)
=sin50cos30-cos50sin30-sin50cos30-cos50sin30
=-2cos50sin30
分母=cos(50-30)-cos(50+30)
=cos50cos30+sin50sin30-cos50cos30+sin50sin30
=2sin50sin30
约分
原式=-cos50/sin50=-cot50