用三角比公式化简：sin50'（1＋根号3*tan10'）

由题意得：方法1：sin50°(1+√3×tan 10°) =(sin50°cos10°+√3sin50°sin10°)/cos10° =[sin(60°-10°)cos10°+√3sin(60°-10°)sin10°]/cos10° =(sin60°cos10°²-cos60°sin10°cos10°+√3sin60°cos10°sin10°-√3cos60°sin10°²)/cos10° =[√3/2*(cos10°²-sin10°²)+sin10°cos10°]/cos10° =(√3/2×cos20°+1/2×sin20°)/cos10° =(sin60°cos20°+cos60°sin20°)/cos10° =sin80°/cos10° =1 方法2：sin50°(1+√3tan10°) =sin50°[1+(√3sin10°/cos10°)] =sin50°[cos10°+√3sin10°)/cos10°] =2sin50°[(1/2)cos10°+(√3/2)sin10°)/cos10°] =2sin50°[cos60cos10°+sin60sin10°)/cos10°] =2sin50°cos(60°-10°)/cos10 °=2sin50°cos50°/cos10 °=sin100°/cos10 °=cos10°/cos10 °=1 因此sin50°(1+√3×tan 10°) 的值为1