1998 USAMO Problems/Problem 3
Problem
Let be real numbers in the interval such that Prove that .
Solution
Let , where . Then we have
By AM-GM,
Note that by the addition formula for tangents, .
So , as desired.
See Also
1998 USAMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |
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