1977 IMO Problems/Problem 4
Let be given reals. We consider the function defined byProve that if for any real number we have then and
Therefore, . Since this identity is true for any real , let the sine term be one, .
To get cancellation on the rightmost terms, note .
Let . Then . Since it's valid for all real let , and we are done.
The above solution was posted and copyrighted by aznlord1337. The original thread for this problem can be found here: 
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