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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

如图

2sin10sin20sin40 =2sin10(sin20sin40) =2sin10[cos(20-40)-cos(20+40)]/2 =sin10(cos20-cos60) =sin10(cos20-1/2) 故 sin10+2sin10sin20sin40 =sin10+sin10(cos20-1/2) =sin10cos20+1/2sin10 =[sin(10-20)+sin(10+20)]/2+(1/2)sin10 =-(1/2)sin...

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

原式=sin10°+2sin10°?[cos(20°?40°)2-cos(20°+40°)2-]=sin10°+sin10°?(cos20°-cos60°)=sin10°-12sin10°+sin10°cos20°=12sin10°+sin10°cos20°=12[sin(10°-20°)+sin(10°+20°)]+12sin10°=-12sin10°+14+12sin10°=14,故答案为:14

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)

(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/...

sin20=2sin10 cos10 原式=(sin30)/(2cos10sin40) sinαcosβ=[sin(α+β)+sin(α-β)]/2 积化和差公式 原式=(sin30)/(sin50+sin30) sin30=(根号3)/2 原式=(根号3)/(2sin50°+根号3) 不知道够不够简

解:这是和差化积公式,如果记不住可以采用如下法解决。sin20+sin40=sin(30-10)+sin(30+10)=sin30cos10-cos30sin10+sin30cos10+cos30sin10=2sin30cos10.sin80+sin40=sin(60+20)+sin(60-20)=sin60cos20+cos60sin20+sin60cos20-cos60sin20=2sin60c...

sin (x + y) = sin x cos y + cos x sin y cos (x + y) = cos x cos y - sin x sin y cos(10+10+10)=cos30=开方三除以2 cos20=cos10cos10-sin10sin10 cos30=cos20cos10-sin20sin10 cos30=(cos10cos10-sin10sin10)cos10-(sin10cos10+cos10si...

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