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sin10sin30sin50sin70=多少 急呀!!!!!

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/sin...

学习要注重过程呀 尤其是理科这道题 可以想到用二倍角公式 化成分式 上下乘对偶式 cos10*cos30*cos50*cos70这样就得到 sin20 sin60 sin100 sin140/16 * cos10 cos30 cos50 cos70其中特殊角得值已知了 剩下的 代换一下就行了 想象就知道了

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/co...

解:设A=sin10°sin30°sin50°sin70°。。。。。。(1) B=Cos10°Cos30°Cos50°Cos70°。。。。。(2) (1)×(2)得AB=sin10°sin30°sin50°sin70°Cos10°Cos30°Cos50°Cos70° =1/2Sin20°1/2Sin60°1/2Sin100°1/2Sin140°(由诱导公式知) =1/16Cos10°Cos3...

sin10°sin50°sin70° =sin10°*1/2(cos20°-cos120°) =1/2sin10°(cos20°+1/2) =1/4(sin30°-sin10°)+1/4sin10° =1/4sin30° =1/8 ∴sin10°sin30°sin50°sin70° =1/2*1/8 =1/16

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

分子 分母 同时乘以 cos10° sin10°×sin50°×sin70° = sin10°×sin50°×sin70°× cos10°/cos10° = sin10°× cos10°×sin50°×sin70°/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

sin10°sin30°sin50°sin70°=1/2sin(90°-80°)sin(90°-40°)sin(90°-20°) =1/2cos20°Xcos40°Xcos80° =1/2sin20°Xcos20°Xcos40°Xcos80°/sin20° =1/2X1/2Xsin40°Xcos40°Xcos80°/sin20° =1/16Xsin160°/sin20° sin160°=sin20° =1/16

答案为;1/2, 4sin10sin50sin70 =4cos80cos40cos20 =4cos80cos40cos20sin20/sin20 =2cos80cos40sin40/sin20 =sin80cos80/sin20 =2sin80cos80/2sin20 =sin160/2sin20 =1/2 其实不止这一种方法,还有很多种,记得给我加分啊,谢谢啊1

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