Question

求值：tan70度*cos10度*(根号3tan20度-1)

Answer 1

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

Answer 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