sin40(tan10-根号3)
问题描述:
sin40(tan10-根号3)
tan70cos10(根号3tan20-1)
答
1、原式=sin40°(sin10°/cos10°-√3)
=2sin40°/cos10 °(sin10°sin30°-cos 10°cos30°)
=-2sin40°/cos10 °]cos(30°+10°)
=-2sin40°cos40°/cos10 °
=-sin80°/cos10°
=-cos10°/cos10°
=-1.
2、原式=2sin70°cos10°(sin60°*sin20°/cos20°-cos60 °)/cos70°
=2cos20°cos10°/cos20 °(sin60°*sin20°-cos60 °cos20°)/cos70°
=[-2cos10°]cos(60°+20°)/cos70°
=[-2cos10°*cos80°/sin20°
=[-2cos10°*sin10 °/sin20°
=-sin20°/sin20°
=-1.