1986 AIME Problems/Problem 3
Contents
Problem
If and , what is ?
Solution 1
Since is the reciprocal function of :
Thus,
Using the tangent addition formula:
.
Solution 2
Using the formula for tangent of a sum, . We only need to find .
We know that . Cross multiplying, we have .
Similarly, we have .
Dividing:
. Plugging in to the earlier formula, we have .
See also
1986 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
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