化简:sin40度(根号3-tan10度)=?

Question

如题所述

Answer 1

sin40(sin60/Cos60-sin10/cos10 )
=Sin40/(Cos10Cos60) (Cos10Sin60-Sin 10 Cos60 )
=Sin40 Sin 50/ (Cos10 Cos60)
=Sin40 Cos40 / (Sin80 Cos 60)
= Sin80/ 2 /(Sin80 Cos 60)
= 1/(2Cos60)
=1

原式=sin40°(tan60°-tan10°)
=sin40°(sin(60°-10°)/(cos10°cos60°))
=2sin40°sin50°/cos10°
=2sin40°cos40°/sin80°
=sin80°/sin80°
=1