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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

10=90-80

sin10+2sin10sin20sin40 =sin10+2sin10sin(30-10)sin(30+10) =sin10+2sin10(sin30cos10=sin10cos30)(sin30cos10+sin10cos30) =sin10+2sin10(1/4 * ( (cos10)^2 - 3(sin10)^2)) =sin10*(1+1/2(cos10)^2 - 3/2 (sin10)^2) =sin10 * (1/2(cos10)^2+...

=-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

原式=sin10*1/2*cos40*cos20 =1/2*2sin10cos10cos20cos40/(2cos10) =1/2*sin20cos20cos40/(2cos10) =1/2*sin40cos40/(4cos10) =1/2*sin80/(8cos10) =1/2*cos10/(8cos10) =1/16

sin(20°) = 0.34202014332567 sin(80°) = 0.98480775301221 sin(40°) = 0.64278760968654 所以这个式子的值就是:0.975042

看结果

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/...

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