sin10°×sin30°×sin50°×sin70°=（ ）.求详解,

这个直接套用三倍角公式
sin(3α) = 3sinα-4sin^3α = 4sinα·sin(π/3+α)sin(π/3-α)
则 sin10°×sin30°×sin50°×sin70°
=sin10°*sin(60°+10°)*sin(60°-10°)*sin30°
=(1/4)sin30°*sin30°
=(1/4)*(1/2)*(1/2)
=1/16

sin10*sin30*sin50*sin70
=cos10*sin10*sin30*sin50*sin70/cos10
=1/2*sin20*sin70*sin30*sin50/cos10
=1/2*sin20*cos20*sin30*sin50/cos10
=1/4sin40*sin50*sin30/cos10
=1/4sin40*cos40*sin30/cos10
=1/8sin80*sin30/cos10
=1/8cos10*sin30/cos10
=1/8sin30
=1/16