作业帮[紧急求助,] 化简:tan70度cos10度((根3)tan20度-1) 辛苦
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 06:40:27
![[紧急求助,] 化简:tan70度cos10度((根3)tan20度-1) 辛苦](/uploads/image/z/6122259-27-9.jpg?t=%5B%E7%B4%A7%E6%80%A5%E6%B1%82%E5%8A%A9%2C%5D+%E5%8C%96%E7%AE%80%3Atan70%E5%BA%A6cos10%E5%BA%A6%28%28%E6%A0%B93%29tan20%E5%BA%A6-1%29+%E8%BE%9B%E8%8B%A6)
[紧急求助,] 化简:tan70度cos10度((根3)tan20度-1) 辛苦
[紧急求助,] 化简:tan70度cos10度((根3)tan20度-1) 辛苦
[紧急求助,] 化简:tan70度cos10度((根3)tan20度-1) 辛苦
tan70度cos10度((根3)tan20度-1)
=tan70°cos10°*(根3sin20°-cos20°）/cos20°
=tan70°cos10°2sin(-10°)/cos20°
=tan70°*(-sin20°)/cos20°
=tan70°*(-tan20°)
=-1
tan70度cos10度(根号3tan20度-1)
=sin70°cos10°(√3sin20°-cos20°)/(cos70°cos20°)
=-2cos20°cos10°sin(30°-20°)/(sin20°cos20°)
=-cos20°sin20°/(sin20°cos20°)
=-1
tan70cos10(√3tan20-1)
=2cot20cos10(√3sin20/cos20-1)
=2cot20cos10(√3/2sin20-1/2cos20)/cos20
=2(cos20/sin20)cos10(sin20cos30-cos20sin30)/cos20
=(2/sin20)cos10sin(20-30)
=(-2sin10cos10)/sin20
=-1
√3tan20-1=(√3sin20/cos20)-1=(√3sin20-cos20)/cos20=2(sin20cos30-cos20sin30)/cos20
=-2sin10/cos20
原式=-tan70cos10×2sin10/cos20
=-(sin20/cos20)tan70
=-tan20tan70
=-tan(90-70)tan70
=-1