用积化和差做
cos10°cos50°cos70°
=0.5*{cos(10°+50°)+cos(10°-50°)}*cos70°
=0.5(cos60°+cos40°)cos70°
=0.5(0.5+cos40°)cos70°
=0.25*cos70°+0.5*cos40°cos70°
=0.25*cos70°+0.5*0.5{cos(40°+70°)+cos(40°-70°)}
=0.25*cos70°+0.25[cos110°+cos30°]
=0.25(cos70°+cos110°+cos30°)
因为cos70°=cos(180°-110°)=-cos110°
所以cos70°+cos110°＝0
所以原式=0.25*cos30°=八分之根号三