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sin50 13tAn10

sin50º×(1+√3×tan10º) =sin50º×(1+√3×sin10º/cos10º) =sin50º×(cos10º+√3×sin10º)/cos10º =sin50º×2(1/2cos10º+√3/2×sin10º)/sin80º =sin50º×2(cos60ºc...

(tan10°-√3)*cos10°/sin50° =(sin10°-√3cos10°)/sin50° =2(1/2*sin10°-√3/2*cos10°)/sin50° =2(sin10°cos60°cos10°sin60°)/sin50° =2sin(10-60)°/sin50° =2sin(-50)°/sin50° =-2sin50°/sin50° =-2

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

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...

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

如图

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

sin50(1+√3tan10) =sin50[1+√3(sin10/cos10)] =sin50[(cos10+√3sin10)/cos10] =sin50[2sin(30+10)/cos10] =(2sin50sin40)/cos10° =(2cos40°*sin40°)/cos10° =sin80°/cos10° =cos10°/cos10° =1

要用到和差化积[2sin50+sin80(1+√3tan10)]/√(1+cos10)=(2sin50+cos10(1+根号3*tan10)]/根号[2*(cos5)^2]=(2sin50+cos10+根号3*sin10)/[根号2 * cos5]=(2sin50+2sin(30+10))/[根号2 * cos5]=根号2*(sin50+sin40)/cos5=2根号2 *sin45*cos5/cos5=2

解:原式=sin50°(1+√3sin10°/cos10°) =2sin50°((1/2)cos10°+(√3/2)sin10°)/cos10° =2sin50°(cos60°cos10°+sin60°sin10°)/cos10° =2sin50°cos(60°-10°)/cos10° (应用差角公式) =2sin50°cos50°/cos10° =sin100°/cos10° (应用倍角公式) =sin(90°+10...

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