Problem:
If tanx+tany=25 and cotx+coty=30, what is tan(x+y)?
Solution:
Multiplying both sides of cotx+coty=30 by tanxtany, we find that tany+tanx=30tanxtany.
Since the left side of this equation is equal to 25, it follows that
tanxtany=3025=65
Therefore,
tan(x+y)=1−tanxtanytanx+tany=1−6525=150
The problems on this page are the property of the MAA's American Mathematics Competitions