来自《耶鲁大学开放课程：基础物理 第16集 第16集》

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  or stranded somewhere in an airport,
  有件非常有意思的事情
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  is to take cosine squared plus sine squared.
  就是将 cos 的平方加上 sin 的平方
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  Squared the whole thing,
  把所有项都平方下
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  add the squared of the whole thing and add them up.
  把两个平方相加 把它们加起来
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  You'll find, by miracle, you will get the 1 from squaring the one
  你会奇迹般的因为这个 1 的平方得到 1
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  and every other power of x will keep on vanishing.
  而 x 的其他幂都抵消了
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  Of course, you'll have to collect powers of x by expanding the bracket.
  当然为了得到 x 的各指数你得把括号展开
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  But it will all cancel.
  但他们会全部抵消
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  That's what I meant by saying this series is as good as this function.
  我说这个级数与这个函数异曲同工就在于此
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  It will obey all the identities known.
  它符合所有的已知特性
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  Okay. Now, for the punch line.
  现在来说一下关键点
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  I think everyone--Some of you may know what the punch line is,
  我想大家...有些人可能知道关键是什么