Difference between revisions of "2012 AIME II Problems/Problem 9"

m (added solution tag, capitalized also)
Line 4: Line 4:
  
 
== Solution ==
 
== Solution ==
 
+
{{solution}}
== See also ==
+
== See Also ==
 
{{AIME box|year=2012|n=II|num-b=8|num-a=10}}
 
{{AIME box|year=2012|n=II|num-b=8|num-a=10}}

Revision as of 14:45, 3 April 2012

Problem 9

Let $x$ and $y$ be real numbers such that $\frac{\sin x}{\sin y} = 3$ and $\frac{\cos x}{\cos y} = \frac12$. The value of $\frac{\sin 2x}{\sin 2y} + \frac{\cos 2x}{\cos 2y}$ can be expressed in the form $\frac pq$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.


Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

2012 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions