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sin10°sin30°sin50°sin70°

sin(90-)=cos 2sincos=sin2 ã 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/sin...

sin10sin30sin50sin70=1/2sin(90-80)sin(90-40)sin(90-20) =1/2cos20Xcos40Xcos80 =1/2sin20Xcos20Xcos40Xcos80/sin20 =1/2X1/2Xsin40Xcos40Xcos80/sin20 =1/16Xsin160/sin20 sin160=sin20 =1/16

sin10sin50sin70 =sin10*1/2(cos20-cos120) =1/2sin10(cos20+1/2) =1/4(sin30-sin10)+1/4sin10 =1/4sin30 =1/8 sin10sin30sin50sin70 =1/2*1/8 =1/16

13sin10sin30sin50sin70⴮ʲô

ĸ ͬʱ cos10 sin10sin50sin70 = sin10sin50sin70 cos10/cos10 = sin10 cos10sin50sin70/cos10 = (1/2) sin20 sin50 sin70/cos10 = (1/2) sin20 sin50 cos20/cos10 = (1/4) sin40 sin50...

sin10=cos(90-10)=cos80 sin30=cos(90-30)=cos60 С90ȵĽa sina=cos90-a

sin10*2cos10*cos20*cos40*cos60/2cos10 =sin20*cos20*cos40*cos60/2cos10 =sin40*cos40*cos60/4cos10 =sin80*cos60/8cos10 =cos10/16cos10=1/16 ֪ҪDz

cos20cos40cos80 =sin20cos20cos40cos80/sin20 =(1/2)sin40cos40cos80/sin20 =(1/4)sin80cos80/sin20 =(1/8)sin160/sin20 =1/8 sin70*sin50*sin10=-1/2(cos120-cos20)*sin10=1/2(sin10cos20+1/2sin10)=1/2[1/2(sin30-sin10)+1/2sin10]=1/4*sin3=...

S=(1/2)sin10sin50sin70=(1/2)[cos80cos40cos20] cos20cos40cos80 ====>>> ӷĸͬ8sin20㣬ʹsin2a=2sinacosa 𰸣S=1/16

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