1977 IMO Problems/Problem 4
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Problem
Let be given reals. We consider the function defined by
Prove that if for any real number
we have
then
and
Solution
.
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: [1]
See Also
1977 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |