sin10sin30sin50sin70=多少

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sin10sin30sin50sin70=多少
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sin10sin30sin50sin70=多少
sin10sin30sin50sin70=多少

sin10sin30sin50sin70=多少
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