tan70°*cos10°(1-√3*tan20)的值

1个回答

  • 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