1.sin40°(tan10°-√3) 2.tan70°cos10°(√3tan20°-1) 3.

1、
tan10-√3
=sin10/cos10-√3
=(sin10-√3cos10)/cos10
=2sin(10-60)/cos10
=-2sin50/cos10

sin40(tan10-√3）
=-(2sin40sin50)/cos10
=-[cos(50-40)-cos(50+40)]/cos10
=-cos10/cos10
=-1
2、
tan70×cos10×(√3tan20-1)
=tan70×cos10×(tan60×tan20-1)
=tan70×cos10×[(sin60×sin20/cos60×cos20)-1]
=tan70×cos10×(sin60×sin20-cos60×cos20)/(cos60×cos20)
=tan70×cos10×[-cos(60+20)]/(cos60 ×cos20)
=-tan70×cos10×cos80/(cos60×cos20)
=-tan70×cos10×sin10/(cos60×cos20)
=-(sin70/cos70)×(1/2)×sin20/(cos60×cos20)
=-(cos20/sin20)×sin20/(2cos60×cos20)
=-1/(2cos60)
=-1
3、
1+√3tan10
=1+√3sin10/cos10
=(cos10+√3sin10)/cos10
=2sin(10+30)/cos10
=2sin40/cos10

sin50(1+√3tan10)
=(2sin40sin50)/cos10
=[cos(50-40)-cos(50+40)]/cos10
=cos10/cos10
=1