Question

高一函数值化简 化简求值 tan70°cos10°.（√3tan20°-1）

Answer 1

tan70°×cos10°×(√3tan20°-1)
=tan70°×cos10°×(tan60°×tan20°-1)
=tan70°×cos10°×[(sin60°×sin20°/cos60°×cos20°)-1]
=tan70°×cos10°×(sin60°×sin20°-cos60°×cos20°)/(cos60°×cos20°) （通分）
=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