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sin10°sin30°sin50°sin70°

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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...

⣺A=sin10sin30sin50sin70㡣1 B=Cos10Cos30Cos50Cos70㡣2 12AB=sin10sin30sin50sin70Cos10Cos30Cos50Cos70 =1/2Sin201/2Sin601/2Sin1001/2Sin140(յʽ֪ =1/16Cos10Cos3...

ѧϰҪעعѽ 뵽öǹʽ ɷʽ ³˶żʽ cos10*cos30*cos50*cos70͵õ sin20 sin60 sin100 sin140/16 * cos10 cos30 cos50 cos70ǵֵ֪ ʣµ һ¾ ֪

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...

sin20sin30sin50sin70= 0.5*2sin20sin30sin50sin70 =0.5sin50sin50sin70 =0.5*0.5*2*sin50sin50sin70 =0.25sin100sin70

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

sin70cos50+sin20sin50 =sin70cos50+sin20sin50 =cos20cos50+sin20sin50 =cos50-20㣩 =cos30 =

Ϊ1/2, 4sin10sin50sin70 =4cos80cos40cos20 =4cos80cos40cos20sin20/sin20 =2cos80cos40sin40/sin20 =sin80cos80/sin20 =2sin80cos80/2sin20 =sin160/2sin20 =1/2 ʵֹһַк֣ܶǵøҼӷְлл1

9/8//Ϊ˷㣬ʡԡ//ǹʽsin3=3sin-4sin³//Σ4sin³=3sin-sin34(sin⁴10+sin⁴50+sin⁴70)=sin10(3sin10-sin30)+sin50(3sin50-sin150)+sin70(3sin70...

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