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sin10sin20sin40化简

观察到自变量间是2倍的关系 考虑用二倍角公式 解:原式=(2cos10 sin10 sin 20 sin40)/(2cos 10) =(2cos20 sin20 sin40)/(4cos10) =(2cos40 sin 40)/(8cos 10) =cos80 / 8cos 10 ∵cos80=-cos 10 ∴原式=- 1/8 希望对您有帮助

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

看结果

=-sin20(cos120-cos40)/2=sin20/4+sin20cos40/2=sin20/4+(sin60-sin20)/4=sin60/4=八分之根号下三

由积化和差公式: sin20°sin40°sin80° =-1/2(cos60-cos(-20))sin80 =-1/4sin80+1/2cos20*sin80 =-1/4sin80+1/2*1/2(sin100+sin60) =-1/4sin80+1/4sin100+1/4*(根号3/2) =(根号3/8)

tan70°=cot20°=cos20°/sin20°, ∴cos20°*cos10°/sin20°+√3*sin10°*tan70°-2cos40° =cos20°(cos10°+√3sin10°)/sin20°-2cos40° =2cos20°sin40°/sin20°-2cos40° =4(cos20°)^2-2cos40° =2(1+cos40°)-2cos40° =2.

(1) sin40(sin10/cos10 - sin60/Cos60) =Sin40/(Cos10Cos60) (Sin 10 Cos60 - Cos10Sin60) =Sin40 Sin (-50)/ (Cos10 Cos60) =-Sin40 Cos40 / (Sin80 Cos 60) = - Sin80/ 2 /(Sin80 Cos 60) = - 1/(2Cos60) =-1 (2)Sin70/Cos70 Cos10 * (Sin 60/...

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

你好 sin30=1/2 sin10cos20sin30cos40 =1/2sin10cos20cos40 =1/2sin10cos10cos20cos40/cos10 =1/4sin20cos20cos40/cos10 =1/8sin40cos40/cos10 =1/16sin80/cos10 =1/16cos10/cos10 =1/16 很高兴为您解答,祝你学习进步!有不明白的可以追问! 如...

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...

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