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