用三角比公式化简：sin50'（1＋根号3*tan10'）
1个回答
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
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