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sin10sin30sin50sin70化简

sin10sin30sin50sin70 = 1/2 * sin10 * sin50 * sin70 =1/2 * sin10 * cos20 * cos 40 =1/2 * cos10 * sin10 * cos20 * cos 40 / cos10 =1/4 * sin20 * cos20 * cos40 / cos10 =1/8 * sin40 * cos40 / cos10 =1/16 * sin80 / cos10 =1/16 * cos10 / cos10 =1/16

因为sin70=cos20,sin50=cos40;sin20=2sin10cos10;sin80=cos10;所以 sin10sin30sin50sin70=sin10sin30sin50cos20=cos10sin10sin30sin50cos20/cos10=sin20sin30sin50cos20/2cos10=sin40sin30sin50/4cos10=sin40sin30cos40/4cos10=sin80sin30/8cos10=sin30/8=1/16

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

sin10sin50sin70=sin10cos40cos20=2sin10cos10cos20cos40/2cos10=sin20cos20cos40/2cos10=sin40cos40/4cos10=sin80/8sin80=1/8

sin10sin30sin50sin70 = 1/2 * sin10 * sin50 * sin70 = 1/2 * sin10 * cos20 * cos 40 = 1/2 * cos10 * sin10 * cos20 * cos 40 / cos10 = 1/4 * sin20 * cos20 * cos40 / cos10 = 1/8 * sin40 * cos40 / cos10 =

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

sin10sin50sin70 =2cos10sin10sin50sin70/(2cos10) =sin20*cos20*cos40/(2cos10) =sin40*cos40/(4cos10) =sin80/(8cos10) =cos10/(8cos10) =1/8

sin10sin30sin50sin70=sin10sin30cos40cos20=2sin10cos10sin30cos40cos20/2cos10=1/2sin20cos20cos40/2cos10=1/4sin40cos40/2cos10=1/8sin80/2cos10=1/16

sin10sin30sin50sin70=(sin10sin30sin50sin70*cos10)/cos10=(sin20sin30sin50sin70)/2cos10=(sin20sin30sin50cos20)/2cos10=(sin40sin30sin50)/4cos10=(sin40sin30cos40)/4cos10=(sin80sin30)/8cos10=(sin80sin30)/8sin80=1/16

cos 倍半角规律 sin10sin30sin50sin70 =1/2cos80cos40cos20sin20/sin20 =1/4cos80cos40sin40/sin20 =1/8cos80sin80/sin20 =1/16sin160/sin20 =1/16sin10sin30sin50sin

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