由sin(90-α)=cosα和2sinαcosα=sin2α得:
sin10sin30sin50sin70
=cos80cos60cos40cos20
=cos80*1/2*cos40(cos20sin20)/sin20
=1/2*cos80cos40*1/2*sin40/sin20
=1/4*cos80*(cos40sin40)/sin20
=1/4*cos80*1/2*sin80/sin20
=1/8*cos80sin80/sin20
=1/8*1/2*sin160/sin20
=1/16sin(180-20)/sin20
=1/16sin20/sin20
=1/16