tan70°cos10°(根号下3tan20°-1)

1个回答

  • tan70°*cos10°*(√3 *tan20° -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 °)

    =-1/4