cos10cot20(√3tan20-1)
=cos10cot20(√3sin20/cos20-1)
=cot20cos10[(√3sin20-cos20)/cos20]
=cot20cos10[2sin(20-30)/cos20]
=-cot20(2cos10sin10/cos20)
=-cot20(sin20/cos20)
=-cot20tan20
=-1