Question

三角函数化简题目。难啊

tan70cos10(√3tan20-1)

Answer 1

tan70cos10(√3tan20-1)
=tan70*cos10(√3sin20-cos20)/cos20
=2tan70*cos10(√3sin20/2-cos20/2)/cos20
=2tan70*cos10(sin20*cos30-cos20*sin30)/cos20
=2tan70*cos10*sin(20-30)/cos20
=-2tan70*cos10*sin10/cos20
=-tan70*(2sin10*cos10)/cos20
=-tan70*sin20/cos20
=-sin70*sin20/(cos70*cos20)
=-(cos90-cos50)/(cos90+cos50)
=cos50/cos50
=1

Answer 2

tan70cos10(√3tan20-1)
=tan70cos10(tan60tan20-1)
=tan70cos10[(sin60sin20/cos60cos20)-1]
=tan70cos10(sin60sin20-cos60cos20)/(cos60cos20)
=tan70cos10[-cos(60+20)]/(cos60cos20)
=-tan70cos10cos80/(cos60cos20)
=-tan70cos10sin10/(cos60cos20)
=-(sin70/cos70)(1/2)sin20/(cos60cos20)
=-(cos20/sin20)sin20/(2cos60cos20)
=-1/(2cos60)
=-1