1996 AIME Problems/Problem 10
Problem
Find the smallest positive integer solution to .
Solution
.
The period of the tangent function is , and the tangent function is one-to-one over each period of its domain.
Thus, .
Since , multiplying both sides by
yields
.
Therefore, the smallest positive solution is .
Solution 2
which is the same as
.
So , for some integer
.
Multiplying by
gives
.
The smallest positive solution of this is