高一三角函数化简求值

原式=2sin20°+cos10°+tan20°sin10°
=(2sin20°cos20°+cos10°cos20°+sin20°sin10°)/cos20°
=(sin40°+cos10°)/cos20°
=(cos50°+cos10°)/cos20°
=(cos30°cos20°)/cos20°
=cos30°
=√3/2
原式=tan70°(cos10°+√3sin10°)-2cos40°
=2tan70°sin(10°+30°)-2cos40°
=2(tan70°sin 40°-cos40)°
=2(cos20°sin40°-sin20°cos40°)/sin20°
=2sin20°/sin20°
=2
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