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sin50 13tAn10

1+√3tan10 =1+√3sin10/cos10 =(cos10+√3sin10)/cos10 =2sin(10+30)/cos10 =2sin40/cos10 sin50(1+√3tan10) =(2sin40sin50)/cos10 =[cos(50-40)-cos(50+40)]/cos10 =cos10/cos10 =1

求值:sin50度(1+根号3倍tan10度) =sin50(1+tan60tan10) =sin50(tan60-tan10)/tan(60-10) =cos50(tan60-tan10) =cos50(sin60cos10-sin10cos60)/cos60cos10 =cos50sin50/cos60cos10 =cos10/(2*1/2*cos10) =cos10/cos10 =1

式子太长不好打,我就分下来解了 sin50°=cos40° cos40°(1+√3tan10°)=cos40°*2*(1/2+√3/2tan10°) =2cos40°*(sin30°cos10°+cos30°sin10°)/cos10° =2cos40°sin40°/cos10° =sin80°/cos10°=1 sin^2 70°=(cos20°)^2=(cos40°+1)/2 (倍角公式)...

因为 tan50°=tan(60°-10°) =(tan60°-tan10°)/(1+√3tan10°) sin50*(1+tan60*tan10) =cos50°*(tan60°-tan10°)*(1+√3*tan10)/(1+√3tan10°) =cos50°(tan60°-tan10°) =cos50°(sin60°/cos60°-sin10°/cos10°) =cos50° (sin60°cos10°-sin10°cos60°)/(cos...

tan40°=tan(30°+10°)=(tan30°+tan10°)/(1-tan30°tan10°) =(√3/3 +tan10°)/[1-(√3/3)tan10°] =(1+√3tan10°)/(√3-tan10°) tan10°-√3=-(1+√3tan10°)/tan40° sin40°(tan10°-√3) =sin40°·[-(1+√3tan10°)/tan40°] =sin40°·[-(1+√3tan10°)/(sin40°/cos4...

sin50°(1+根号3tan10°) = sin50°(cos10°+根号3sin10°) / cos10° = sin50° * 2(cos60°cos10°+sin60°sin10°) / cos10° = sin50° * 2 cos(60°-10°) / cos10° = 2 sin50°cos50° / cos10° = sin100° / cos10° = sin(180°-80°) / cos10° = sin80°...

tan10-√3 =sin10/cos10-√3 =(sin10-√3cos10)/cos10 =2sin(10-60)/cos10 =-2sin50/cos10 sin40(tan10-√3) =-(2sin40sin50)/cos10 =-[cos(50-40)-cos(50+40)]/cos10 =-cos10/cos10 =-1

tan10°-√3=tan10°-tan60°利用公式tanα-tanβ=sin(α-β)/(cosα·cosβ)得tan10°-tan60°=-sin50°/(cos10°cos60°)(tan10°-√3)×cos10° /sin50°=(tan10°-tan60°)cos10°/sin50°=[-sin50°/(cos10°cos60°)]cos10°/sin50°=-1/cos60°=-2

解:sin50°(1+√3 tan10°)-cos20°/cos80°√(1-cos20°) =[sin50°(cos10°+√3 sin10°)/cos10°-cos20°]/√2sin²10° =(1-cos20°)/√2sin²10° =√2

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